In Python

1+ 4. Numerical Integration (a) Write a program that will estimate a definite integral using the Rectangle rule. The inputs should be the interval [a, b] and the number of divisions N. Test your program by estimating the value of So 11. dx using N = 10. Compare to the exact value and comment on the accuracy of this program. (b) Write a program that will estimate a definite integral using the Trapezoidal rule. The inputs should be the interval [a, b] and the number of divisions N. Test your program by estimating the value of S. dx using N = 10. Compare to the exact value and comment on the accuracy of this program. (c) Write a program that will estimate a definite integral using the Simpson's rule. The inputs should be the interval [a, b] and the number of divisions N. Test your program by estimating the value of Sof dx using N = 10. Compare to the exact value and comment on the accuracy of this program. 1+x 1 1+2