Question 8 e* then the integrand is the same as dx In 4+e¬* 4e* +1 A True B) False - 3 ÷+C, then f (x)= x4 (A) True (B) False

Q: Question 2 Integrate: 16x 10 dx 4x2- 5x + 81

A: Given,         ∫16x-104x2-5x+81dx

Q: xe* dx (x + 1)2

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: Find dr/d0. 10) e1/3 – r1/3 =1

A: Given query is to find the derivative.

Q: 2+ex dx ex Evaluate:

A: Topic = Integration

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: -1 Integrate Jxsin 'dx

A: To evaluate : ∫01x sin-1x dx

Q: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

A:

Q: Integrate from 0 to 2

A:

Q: e' [ S (5² +a²) 2 ] = t sinat 2a 7 Prove using Convolution

A:

Q: Evaluate p* sin 0 de dr.

A:

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Evaluate [²√₁-Pa dx °ex√1_(ex)2 ofile कस 0 √i-(ex)

A:

Q: %3D Evaluate the fo llowing intergrals nest_x5 dn.

A: Solving by definite integral we have

Q: Ql Find se dx |

A:

Q: Find the cosine of ZF. G 22 cos (F) √55 H = 33 Write your answer in simplified, rationalized form.…

A: To determine the cosine ratio

Q: In x2/25+ x² dx , we let x = 5sine. (A) True False

A: FALSEHere , the correct substitution is x=5tanθ differentiatate On both sidesdx= 5 sec2θ…

Q: Evaluate x* (1-x3)0/2 dx Select one: 3*1*3*1 , T 8*6*4*2 2 O None 3*1*3*1, T 8*6*4*2 4 7*5*3*1, T…

A:

Q: 1 dx ½ x* -1 1 a) arctan -In 3+ 3 4 8 1 b) -arctan 3 --In 2+ 3 4 8 c) -arctan 3 +-In2+ 4 8 1 1…

A:

Q: 1. * dx a <-I 94 dx, a<o

A: (1).  The given integral is: I=∫1∞ xa dx  ;           a&lt;-1

Q: 2) Evaluate: 6+ 1-x² i) dx

A: