4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

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: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

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

A:

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

A:

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: 1. cosysin2xdx + (cos²y – cos²x)dy = 0; by treating x as the dependent variable

A:

Q: =7 (1+ cos(t*)) dt. Find g'(z). COS x2

A: g'(x)=ddx(∫x26(1+cos(t3))dt) using fundamental theorem of calculus…

Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10. 3 J√cos z sin ³ zdz COS

A:

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: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

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.…

A:

Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

A:

Q: 22 3x'y = 2ty- 3). 23 (2y cos x + sin* x) dx sin x dy; when x Ans. y= cty- 3) exp (x n, y = 1. %3D…

A:

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)…

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

A:

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: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

A:

Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

A:

Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

A:

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

A:

Q: ,2 Compute x² cos(x³ + 3) dx

A:

Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

A:

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

A:

Q: Show that where n is a positive integer.

A: To show

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: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

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

A:

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

A:

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

A:

Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

A:

Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: F.(3e-3 sin(2x')) is equal to 2 3. n 4+@² 3 cos 8 4 3. 7(1+o² 4 cos 4 4 1 3, 1 +4cos 4. 4 2 1+@ 4…

A: Use the following formulas to calculate the Fourier cosine transform. Fee-ax=2πaa2+ω2…

Q: 3. Find the general solution of (2y cos x + sin*x)dx = sin x dy a. y = sin²x(- cos x + C) c. y =…

A: follow next step

Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

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: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

A:

Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: 0.5 COS T - In(4 sin z) dz. J0.1

A:

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

A:

Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

A: