Sin'z dz 4.

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

A:

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: sec?x Integral tanx

A:

Q: Prompts Ssin(3x)sin(4x)dx

A:

Q: Evaluate

A:

Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

A:

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: 2 9) -sinh? -cosh -dz

A:

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

A:

Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: 2 cosh(2x) – sinh(2x) = 2

A:

Q: Sinh) esechct) dy

A:

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: Find dy ду é^sinx in sx

A:

Q: Integrate Sin (1-2 In v)

A: The detailed solution is given below Thank you

Q: Integrate  dy/dx sinx=1

A: We know, ddxcosec x = -cosec x·cot x ddxcot x=-cosec2x ddx(cosec x-cot x)=-cosec x·cot x + cosec2x…

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

Q: sec Vn du in

A:

Q: = Solve: Cony siny dx + dy. cosr sinx

A:

Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

A:

Q: y'' + 3y' + 2y = sin ex

A:

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

A:

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

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

Q: 2. Jx sinh x2 dx

A: ∫x sinh x2 dx

Q: 4 + sinh(3x) = 4 cosh(3x).

A:

Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: 3. In (cose) tane de

A:

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: integrate 1/(sin^2(3x) dx

A:

Q: Integrate: Jez sin(3x) dx

A: Solve the integration by substitution method

Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: cosh(In x) dx

A:

Q: sin³€ dt to ylomeldon 3.

A:

Q: (7 – siny)y' = 3x2 + 2x

A:

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: sin 2x dx 4. J2osin cosmetin2xdx

A:

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

A:

Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

A: