15. sin x + cos y = sin x cos y

Q: Evaluate the definite integral.

A: Given : The definite integral is ∫π 3π 2  cos x ( sin x )sin2 x -14 dx .

Q: 1- Calculate the value of y if: a-y= sin "(0.25) + sinh (2). b- y= sinh (15)+cosh"(31)

A: Note: According to our guideline, we will answer one question. As the exact one is not specified.…

Q: 25. y = x² sin“ x + x -2 = x* sin' x + x cos

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Q: 5. (e* sin y – 2y sin x) + (e* cos y + 2 cos x)y' = 0

A:

Q: 2. Find y': sin(x+y)% y2 cos x.

A: As per our guidelines we are supposed to solve only one question i.e. the question number 2 . Which…

Q: 9. Sin 2X dx COS 2X

A:

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: y = sin' x- cos 3 – cos' x cos³

A:

Q: 2 + sin x Differentiate Y x + cos

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Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

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: 7/2 S 3 cos (x) sin°(æ) dx =

A:

Q: 12) * 1 Differentiate y =sinh

A: Given:y=sinh212x

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: 2. 2 | sin xcos xdx

A:

Q: 15. For fe' cos x dx, what is du? cos x e' dx - sin x dx G(e* cos x + e" sin x) + C

A: The given question can be solved as shown in step2.

Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

A:

Q: 9. e' cos (x) =1+ sin (xy) 10. tan (x – y) = 1+ x2

A: Given the equations 1)ey cos(x)=1+sin(xy)2) tan(x-y)=y1+x2We need to find implicit differentiation…

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

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: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

A:

Q: 4. ſ cos xesinx dx

A:

Q: 1. [* sin' y cos' ydy 3

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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Q: 1/2 sin 12 y cos' y dy y

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Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: 4. sin M= 20 16 30 5. tan L = 6. cos Z = 16

A:

Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.

Q: 2 2 | sin x cos xdx X,

A: As per our guidelines we are supposed to answer only one question kindly repost the other question…

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

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- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh (15)+cosh (31)

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

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

A:

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

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Q: 8. (e sin y + 3y) (3x - e" sin y)y' = 0

A:

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: 11. x² - y? = 7 12. x sin y - y sin x = 0 13. x cos y +y cos x = 0

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Q: y 2+ TT 3 2 -2+ -37

A:

Q: 4) Find when y2 – x² + cos(x + y) = 0

A:

Q: 36) y = 2 sin x - 4 10+y 8-

A: to find the differentiation of given function.

Q: If y=a cos ( sin x) +b sin (sin x :) then y" + (tan x )y'+ cos'x = 0.

A:

Q: 3 5. cos x dx > 6. sin x cos x dx =

A: According to the trigonometric ratio:  sin2x + cos2x = 1 Integration of cos x is sin x.

Q: 13. y = -3 sin 2mx 15. y = -sin ix 14. y = -2 sin mx 16. y = -sin jx

A:

Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh'(15)+cosh (31)

A: according to the guidelines of bartleby I will do only first question please ask rest of the…

Q: 7+2 sin y -dy = D cos ?y

A: on solving this we get the

Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

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: