2. Integrate the following function (a) analytically 3. I- fxe2* dx and numerically using n = 4 (b) Trapezoid Rule (c) Simpson's Rule. Compute the percent error for both numerical integrations using the analytical value as the true value.

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A: We will use the method of separation of variables and then integrate.

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A: Topic  - differentiation by parts

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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.