2²dx Evaluate: 4 – x2 - A f (x) = 4 sin (5) + xV4- a2 +C 2 2 sin- () – xv4 – x² +C В f (x) = 2 © f(x) = 2 sin (5) + xvV4 – a2 +C 2 D None of the above 4 sin () – xv4 – x² +C E f (x) = 2

Q: Evaluate: (9 - 22) -1 x- V9- x sin A f (z) = %3D V9-2 None of the above a+V9-r sin ©f(z) = V9-7 9-…

A: We have to choose the correct option from the given options according to the given information

Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

A:

Q: Evaluate f{ [sec (x) + csc (x)] + sin ()} dx : (2)]? + sin (팔프)}dz O a. tan (x) In |csc (2æ) + cot…

A: To solve the following integral

Q: Let f(x) = sin(2x) + cos(x) then f"(x) Select one: O a. 4sin(2z) + cos(z) O b. -sin(2x) – cos(x) Oc…

A:

Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

Q: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

Q: 13 |xsin xdx ーT 15 (xsin xdx

A: I=∫ x sinx dxIntegration by parts;u=x, v=sinxI=x∫sinx dx-∫(1 ∫sinx dx) dxI=-x cosx +∫cosx dxI=-xcosx…

Q: Which of the following equations does not hold for all values of x and y? cos(r + y) = cos(x) cos(y)…

A:

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

A:

Q: The Wronskian of two differential functions f and g is W(f.g)=fg'-gf, more formally, f(x) W(f,g)(x)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…

A: MULTIPLE QUESTIONS:   “Since you have asked multiple questions, we will solve the first question for…

Q: Evaluate: /x?cos(2x)dx 2x2sin(2x) + 2xcos(2x) – sin(2 x) А + C 4 2x2sin(2x) – 2xcos(2x) – sin(2x) +C…

A:

Q: Evaluate / 3 x sin(x)dx 03 (sin(x) – x cos(x)) + c Osin(x) – x cos(x) + c 03 x sin(x) + 3 cos(x) + c…

A:

Q: Evaluate ſ x³ {/ (1 + x³)² dk

A:

Q: XV3X-4 V3x-4 +C tan 3x-4 +C sin' 2 tan 3x-4 +C sin 3x-4+ C None V3x=4 tan +C 2

A:

Q: Evaluate / 11 x cos(x)dx O11 sin(x) + 11 x cos(x) + c Oc – 11 (x sin(x) + cos(x)) Ox sin(x) – 11…

A: Topic- Integration

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Let F= (2e", 5 sin(x), 8 cos(x)). Calculate div(F) and curl(F). (Use symbolic notation and fractions…

A:

Q: Integrate the function. 2+81 dx 4x2 V In Vx2 + 81 + x x2+81 4x + C In Vx2 • 81 + x] Vx2 + 81 + C 4x…

A: Given,            ∫x2 + 814x2 dx

Q: 9. The value of f 1-x 1+x A. sin ¹¹x + √1 + B. sin¹x - √1 + dx x² + C x² + C C. sin ¹¹x + √1- x² + C…

A:

Q: Find a suitable substitution for evaluating ∫tan x sec2 x dx andexplain your choice.

A: we have to integrate the following integral using a suitable substitution. ∫tanx.sec2xdx

Q: Integrate the square root of sin (In x) dx * O x/2 [ sin (Inx) + cos (Inx)] + C x/2 [ sin (Inx) -…

A: Given

Q: Use substitution to evaluate the integral 4 sec2 4xvtan 4xdx 4 (tan 4x) + C 3 15 (tan 4x) + C 2 (tan…

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

Q: Find 7s + 15 -7 s2 + 2 15 cos (v2t) + 7 sin(v2t) V2 7 cos(V3t) + 15 sin(3t) V2 7 cos (v2t) – sin(vZ…

A:

Q: (b) Verify that f(x) = 2 cos(x) sin(1x). f(x) = sin(6x) + sin(7x) = 2 sin = 2 sin 6x + N 2 X COS 6x…

A: Given