14. Evaluate cos 3x+ dx. 2

Q: (a) Evaluate| cos (4x) -dx. (1+ 2sin ( n(4x)*

A:

Q: s nip

A: Given: 12cos2x+C=14cos2x

Q: Suppose = cos 4- Evaluate: |dx A - 3sin sin x-4+ C © -)+c -x- 3 3sin

A:

Q: 7x Cos + COS cos 2.

A: According to trignometry formula:cos a +cos b =2cosa+b2 cosa-b2Given,cosx2+ cos7x2a=x2; b=7x2

Q: 15. Evaluate 2 (3x + cos 4x) dx

A: The given integral is: I=∫0π2 3x+cos(4x) dx

Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

A:

Q: 1/12 cos 2x dx

A:

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

A:

Q: 7T then 6. If 0 = sin(0) = cos(0) = COS %3D

A:

Q: Differentiate implicitly cos(x³y³) = 9

A: Given,         cosx3y3=9

Q: 2+7 sin cos z zp-

A: Given: ∫2+7sin3zcos2zdz

Q: 2. Estimate cos (– 0.1) + cos 4

A: As per given question  We have to solve above question

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: TO 2 8. х cOs 2x dx

A: We have to calculate the given integral   The given integral is

Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: 25+16 x² (2, Sinx 3 + Cos? x xp 2

A: According to the fundamental theorem of calculus ∫f(x)dx=F(x), where dFdx=f(x). The definite…

Q: 4. Evaluate et cos xdx.

A:

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

Q: a) |(4 cos x+2cos x– 1)dx

A: we know the following identities   ∫cos(x)=sinx

Q: 2 Cos 4xdx

A: The objective is to find the value of given integral.

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: In(1+cos 3x) +C dx 3. 1+cos 3.x

A: Differentiate of the RHS the we get RHS

Q: .3 4 cos³ 4y /sin 4y dy

A: To find out the integration.

Q: For | cos 3x cos 4x dx :

A:

Q: Evaluate •2 (23 1 4 – x² dx Cos 27 1 2

A:

Q: 5. Evaluate 1. S, sin(x2) dx

A:

Q: 2. Evaluate 2 sin1ºx cos0x dx.

A:

Q: 22 Evaluate s cos (Iz)e dz

A: Formulae used: ddxcosx=-sinxddxsinx=cosx∫eaxdx=eaxa∫cosxdx=sinx+C By party integration formula…

Q: 1. Evaluate the integral 7/2 cos xesinx *dx

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Q: Evaluate COs 2 4 – x² dx

A: use the property of even function and odd function to evaluate the integral.

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

Q: 5. Evaluate 1. , sin(x?) dx

A: #1 intregal

Q: 22: Evaluate Sea s cos²(y s) ds.

A: Solution:-

Q: 4. Use Walli's formula to evaluate 2 sin*x cos°xdx.

A: Given integral is as below:-                  ∫0π2 sin4xcos9xdx

Q: 2 Evaluate: [5 cos(5)x – 5 csc² (x) ] dx COS

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Q: 4 cos* 3xdx

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: If fex) cos cmx) dx = and %3D fox) E Coscn'x) then %3D COS n3 +! KIN

A:

Q: 10. 4 COS dx 2

A: the given integral is: ∫cos4x2dx we have to evaluate the given integral.

Q: dx Evaluate 6e* cos (3e *) -In |sec(3e ) – tan(3e |] + C O 2 [In |sec(3e-x) + tan(3e-)|] + C -18 [In…

A:

Q: Evaluate: Je*cos(7e*)cos(4e*)dx.

A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

Q: 1. S 3 cos("/x) x2

A: "Since you have asked multiple questions , we will solved the multiple questions for you. If you…

Q: Evaluate cos (4x) dx.

A:

Q: Differentiate  cos(t^2 - 6)

A: Given: cost2-6

Q: ∫√(1+2sin3x) (cos3x)dx

A: