3. Consider the curve y = x°. (a) Write down, BUT DO NOT EVALUATE, the integral that gives the length of this curve of the interval [0, 1]. 4 rectangles to approximate the (b) Use a Riemann sum with n = integral you wrote down in part (a).

Q: Use Simpson's to approximate the integral 2+x* dx, n=4.

A: The integral is ∫012+x4 dx, n=4

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.