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

Q: 1. 6(x) = e- sin a, for y' + y cos x

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Q: 2 y = A cos 4x + B sin 4x +sin 3x b) 7

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Q: Solve the fllowing D.E +4y= cos x - sinx 2. CoS X %3D

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Q: 2 6. dx (sin x – cos x)?

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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

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

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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: Consider b. () 2: x dx e-2 sin 5 a

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Q: (b) I cos cos(√x + 3) dx

A: b Given integral is ∫cosx+3dx. We have to solve the given integral. Use formula…

Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

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Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: 1 dx x +c, find- dx exactly where c is a constant. 5. If 1+cos x = tan 2 X 3+3 cos 4 n dx tam S c /+…

A: It is given that

Q: 1(y) = In(sin(cos(y²))) %3D

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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: 2. Find cos ec (In x) dx . x1+ cot(h x)

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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: (d) lim In(cos r) エ→0

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Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: b) S. cos x cos 7x dx

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: cos 3x b. S; dx = ... 3+15 sin 3x

A: We have to solve the given integral .

Q: 1o² (sin x + cos x)dx = O 2 O None O 1

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Q: 2 dx (a) t = tan x. %3D 5+4 cos 2x 0.

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Q: 1 dx 3 sin x+4 cos x+3

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Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

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Q: 11. sin(x) + cos(y) = ey

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Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

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: 1 dx J 3 sin x+4 cos x+3

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Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

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Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

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Q: Evaluate D°(cos x +e-2") A cos x – 32e-2x (B) sin x + 64e -2x (c) - sin x – 32e -2r (D - cos x +64e…

A: Here we have to evaluate      D6(cosx+e-2x)

Q: 1. (a) Find sin 6x+ cos 4x dx. (b) Evaluate dx. Hence, solve dx. (e' +2) (e'+2)

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Q: 5 cos(a) sin (x) dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: cos x 6) dx is equal to sin x A. In/2 В. Inv3 C. In" D. In e

A: The  given integral is ∫π4π2cosxsinxdx

Q: E valuate dx 7-3 Sin X +6 Cos X

A: solution.

Q: 8. Evaluate (a). (20-0y di (b). / COS I sin(sin x) dx -3

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

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Q: 1. Please answer the following questions. a) [x-In (4x²) dx b) ſe* *. cos (2x) dx c) [In (x² +2) dx…

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Q: dy.xandy in =cos = COS e

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Q: 7/2 d sin dx dx COS

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below