1 (a) Calculate and fully simplify |a² cos(z) dz.

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

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Q: 8. (t² + 3) cos(5t) dt

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Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: 4. | e2x cos 3x dx

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: 211 211 cos nx dx= [cos %3D %3D nx cos nx dx =0.

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Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

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Q: | Cas (41 - ) dt (a) (b) Cos* () Sin () dx

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Q: Example 1 Find dy/dx, if sin (²+3x+¹) b. y = cos²(2x-1)

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Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

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Q: 3. Explain graphically: cos x dx = 0.

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Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: 2- The integration of f x²sin (x³). dx is: (a) cos (x³) + C (b) cos (x³) (e)금 cos (x3) + C (d) 글 cos…

A: According to the bartleby guidelines, for more tan one question asked only the first question should…

Q: dx = 1– cos(bx) Select one: a. br – In sec(bx) + tan(bx)| + C b. – csc(bæ) – cot(bæ) + C - - In |1 –…

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Q: Evaluate the integrals in Exercises

A: Question 7 - Let the given integral be y - y = ∫lnx-5x-5dx       ............(1)Let,t = lnx-5…

Q: The value of A.cos(x²+)+C cos (x² + + C fx sin (x²+3) de dx B. - cos (x² + 5) + C D. -cos (x²+)+C

A: Option (B)

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: 3e" + 3x + 10 cos x + 2)dx .2

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Q: 19. Determine the period and phase shift for y = cos(5x + n).

A: We can find the period and phase shift as below using the general equation of wave.

Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Take the derivative of this integral.

A: Given

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: 450 400 AA 350 300 250 200 150 100 50 -4 -50 8 16 24 28 36 12 20 32 -100 -150 -200 -250 -300 Dy =…

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Q: ution of y" + 4y = cos 2x b

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Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

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Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

Q: Determine the general solution of y' = cosx cos y

A: we have to find the general solution

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

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Q: 11.| V1- сos 2x dx COS

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

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Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: 7/2 d sin dx dx COS

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Q: Sväsin(x³/2)dx= 2 들Cos(x3/2) +C A 2 -을cos(x3/2) + C B 2 O -2cos(x³/2+Cc) C D) 을/Xcos(x3/2) + C

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Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: 20. e2= cos(z/4) dz

A: