Q1)Evaluate the following integral: 2 2x2-x dx 2x2 +3x

Q: Evaluate the integral dx 2e 2x 3e2x

A: We have to find the value of integral: ∫ex2e-2x-3e2xdx Rewriting the given integral,…

Q: Evaluate the integral: 3xe-/4 dr

A: we will do it by integration by parts ∫uv=u∫v-∫u'∫v

Q: Evaluate the integral: a V1 + 492 da

A:

Q: Evaluate the integral: 5x/8x² – 1 dx - 5 (8x2 – 1)- + C (8a? – 1)-+ C (822 – 1) + C -(8x2 – 1) + C 8…

A:

Q: 2x 35. x2 + 6x + 13 -бх + 13

A:

Q: 1 / (2x+ 3)10 dx

A: The given integral is ∫12x+310dx Calculate the integral of the value.

Q: Use Table shown to rewrite as the difference of two integrals.

A: Given integral, ∫162x3-4xdx          ...(1)

Q: 8. Evaluate the integral 4 + 6x dx Vx

A: In this question we have to solve the integration given. we can write , x=(x)12

Q: Evaluate the following integral: Sov (v² + 6 Vi7 - 3 V -)dv -) dv 3y2

A:

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.