1. 3sin x = sin-' (3x – 4x³), xe 2 2.

Q: 1. Find the derivative 4 ln 2) ³ 3x³ sin(2x) 5x2+3

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Q: 7) x sec (x)dx

A: We will solve the problem

Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: D cos( 5t D sinf see Dcost cast) 4

A: See the attachment

Q: *T/4 sec² xdx 26. 27. sin xdx TT 28. COS xdx

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Q: 4x x*e*dx (2sin dx V4-x2

A: We can solve all the intregration problems with tha mathod of substitution. In substitution we use a…

Q: 4. Solve sin (2-) = 1.

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Q: 2x fe²x sinx dx

A: Using integration by part.

Q: Poaineter Soe y' ty = cof x

A: we have to find the differential equation by using variation of parameters.

Q: 2 sec2( sec-1x)dx xVx² -1 3. 3.

A: Here  we evaluate    ∫32 sec2sec-1xxx2-1  dx

Q: 2. 2 | sin xcos xdx

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Q: d? -(sin-'(x²)) dx2 2– 4x4 A 3 2– 2x4 B 3 2+2x4 3. 2+4x4 D

A: Here we have to use the concept of derivative

Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

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Q: (a) [- 9x2 +x° cos x dx = 3

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

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Q: x* + 4 dx : %3D 3

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Q: 2x – sin y y' = x cos y

A:

Q: 4)y = 2 sin (3x +) - 1

A: Given: y=2sin3x+π5-1

Q: +3x2 b. Find (y)? = sin³(cos³(* *3*)) %3D dx 2

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Q: 3. sín 4x √1-16x² dx

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Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 1 dx 2 21+2*2 ху

A:

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: dx Evaluate V- x² – 4x – 1

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Q: #1) Solve: 2 cos²x − cos x = 1 on [0,2π) —

A: Given ,  2cos^2(x) - cos(x) =1 on [0,2pi)   Substitute  u  for  cos⁡(x) .  2(u)2−(u)=1…