ompute the following integral, with poles and emainders.

Q: Find or evaluate the integral by completing the square.

A: Consider the polynomial: ax2+bx+c. We try to obtain an expression of the form, kx+d2+e from the…

Q: f sec¹ x dx

A: Integrate the integral sec7x .

Q: Evaluate the.integral (x+y+2 dz olyde

A: Evaluate the given integral as follows. ∫01∫01∫01x2+y2+z2 dz dy dx=∫01∫01∫01x2+y2+z2 dz dy…

Q: Evaluate the integral. 1 dr 25 + r2

A: we will let  25+r2=t2        to solve this question.

Q: [x² Arctan(x) dx

A:

Q: construct vw so that v= 2ab?

A: Here VW  and AB are line segments . To construct VW ,so that VW=2AB

Q: 1 2 S S xe dx dy ху хе 0 -1

A:

Q: (1) (2) La (10— 2х) dx xdx

A:

Q: the cente C is circ le to a of orgin Coordinates and vadius 2

A: I have solved using residues

Q: Find or evaluate the integral by completing the square.

A: Our Aim is to evaluate the integral given below :-∫1-x2-4xdx -(i)

Q: -x Jez е sin x dx

A:

Q: 5 10 √2 (h) A = 10 2 α ; discuss your answer in dependence on the value of the parameters √2 a a,…

A:

Q: T.h.J unitorm (x) is ィマ Conrinu ous [', 00)

A: It is given that ;            fx = 1x2   for  x ∈ [1, ∞) To prove :  f(x)  is uniformly continuous…

Q: ) 1 1 dx x – 1

A:

Q: 1 -1 4 | 1 4 -2 (a) Let A = 1 Find an orthonormal basis of col(A). 4 2 -1 (b) Find an orthonormal…

A: First we need to find answer of part (a) to solve the part (b) question:-

Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

A: The integral can be modelled by calculating the intersection points of the curves. The intersection…

Q: Write the integral in terms of u and du. Then evaluate.

A: To solve the indefinite integral.