1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

Q: 3 S² x³ cos x ²dx 6.

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Q: Suppose that 1 a + sin x ) dx = 15x 1 + x2 -1 What is the value of a Your answer should be an…

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Q: 17. 18. 19. dx/ (9x² + 4) sin³ x cos x dx (secs x) dx / csc x

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

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3*) 4. y = cos 2x (e*²-1)…

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

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

Q: 7/4 Q6// S*x cos3 2x sin* 2x dx

A: we have,

Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

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Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 2. Vsin 3x cos 3xdx

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

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: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: 1. y = In (3 – 4 cos x) + (4x – 5)5

A: 1). Given function is y=ln3-4cosx+4x-55. To find: dydx Solution: Power rule of differentiation…

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: 11 Evaluate ff sin(y²)dydx where 2: 0<y <1, 0<x<y°. 0x a) 1-cos(x) b) (-cos(x)) --cos(1) d). cos(1)…

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Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

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Q: 11 Evaluate || sin(y)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) 1 b) (1–cos(x)) e) ,-cos(1) d) 1…

A: This integral can be solved by changing the order of the integral. The order can be changed by…

Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: 1(y) = In(sin(cos(y²))) %3D

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Q: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ x.

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: Question 7 Calculate the integral: /x' cos (2.x²) dx 1 o- sin(2x³) + r cos(2r*) + C b) O sin(2r*)…

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Q: 1.4 The integral 2 sin (15ax) sin (10a.x) dx equals: (a) (cos (5ax) – cos (25ax)) da (b) (sin (5ax)…

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Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: If y= x2 sin 2x, then y = А) 2х cos 2x B 2x (sin 2x - x cos 2x) C 2x (sin 2x + x cos 2x) (D) 4x cos…

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Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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

A: Differentiate of the RHS the we get RHS

Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

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

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: 7/2 in° x cos' xr dx 4

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Q: 1) fcoe cos x sin rdr

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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

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Q: 1 find the value of so that ky"=-1 at y= For cos x- sin y=- O V3 2 4 4

A: Solution:-

Q: Question 6 Compute the following integral: sin (8z) de 1 4 a) cos(8x) sin*(8x) + C 32 1 cos (8r) + C…

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Q: -1 (x³+y³ ,3. then xdw dw +y dy If w = tan x-y sin(w) sin(2w) cos(2w) None of these

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