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DerivativeAndIntegralProblem.java in the folder lectures/week1_2 of the course site.

import java.util.Scanner;

public class DerivativeAndIntegralProblem {

public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

int n = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();
int[] coefficients = new int[n + 1];

for (int i = 0; i <= n; i++) {
coefficients[i] = scanner.nextInt();
}

int derivativeValue = calculateDerivativeValueAt(coefficients, n, a);
int integralValue = calculateIntegralValueBetween(coefficients, n, a, b);

System.out.println(derivativeValue);
System.out.println(integralValue);
}

public static int calculateDerivativeValueAt(int[] coefficients, int n, int x) {
int result = 0;
for (int i = n; i > 0; i--) {
result += coefficients[i] * i * Math.pow(x, i - 1);
}
return result;
}

public static int calculateIntegralValueBetween(int[] coefficients, int n, int a, int b) {
int resultA = 0;
int resultB = 0;
for (int i = n; i >= 0; i--) {
resultA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
resultB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return resultB - resultA;
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFromAToB = calculateIntegralFromAToB(coefficients, a, b);
System.out.println(integralFromAToB);
}

// Method to calculate the derivative of a polynomial at a given point x
private static int calculateDerivativeAtX(int[] coefficients, int x) {
int derivative = 0;
for (int i = coefficients.length - 1; i > 0; i--) {
derivative += i * coefficients[i] * Math.pow(x, i - 1);
}
return derivative;
}

// Method to calculate the integral of a polynomial from a to b
private static int calculateIntegralFromAToB(int[] coefficients, int a, int b) {
double integralA = 0;
double integralB = 0;
for (int i = coefficients.length - 1; i >= 0; i--) {
integralA += coefficients[i] * Math.pow(a, i + 1) / (i + 1);
integralB += coefficients[i] * Math.pow(b, i + 1) / (i + 1);
}
return (int) (integralB - integralA);
}
}import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Read the number of coefficients
int n = scanner.nextInt();

// Read the coefficients into an array
int[] coefficients = new int[n + 1];
for (int i = n; i >= 0; i--) {
coefficients[i] = scanner.nextInt();
}

// Read the point to evaluate the derivative and the bounds for integration
int x = scanner.nextInt();
int a = scanner.nextInt();
int b = scanner.nextInt();

// Calculate and print the derivative at point x
int derivativeAtX = calculateDerivativeAtX(coefficients, x);
System.out.println(derivativeAtX);

// Calculate and print the integral from a to b
int integralFrom