(i) Find the Cauchy principal value of the integral dr. +4z + 8

Q: 1. Compute the integrals. a. L² see 0 sec¹r tan³ r dr

A:

Q: ou provide the solution to get the integral after substi

A: Comparison Test for improper integralsIf  on the interval  thenIf  converges then   also…

Q: Show that the matrix A given below is singular. A = -2

A: A matrix is singular if it's determinant is zero.

Q: I) S dx/ (x² + 4x + 3) find integral

A:

Q: 2. / x + 4x x + 4x +13 dx

A:

Q: integral of 70/t+9

A: Integrate the following function with respect to “t”.

Q: n Σ sin n i=1

A:

Q: 8a + 20x dr. x* + 5x² + 6 Evaluate the definite integral

A: We can evaluate the integral as below.

Q: . Evaluate the following integral or show that they diverge. ekz L (ebe + 52 de 5)²

A: Given query is to find value of the integral.

Q: Evaluate the integral [5x/( x²+1)(2x-2).

A: Given, the integral

Q: o f dx/ (x² + 4x + 5) find integral

A:

Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

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.