sin30 de 10. J 1-cos e 11. J sin 20 sin 40 de. cos?30 d0 12. S 1 -cot 30 13. J tan 50 d0. 14. S csc2 In x dx. 15. S ( tan+ cot dx. X X )² dx. 3

Q: Q1: * Evaluate: xe*dx? 1 Add File Q2: Using Trig. substitution: * Evaluate: -dx? 1 Add File Q3:…

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

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A: Differential equations

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: The solution is given in the next step.

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A: The given integral is ∫x dxx2+x2-1-1. We have to change the integral using substitution.

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A: Let's transform integral by using trigonometric substitution.

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Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

Q: 5. y' = x' – 2xy; when x = 1; y = 2 =-1- 2r cose = cosx cos? t 8. y(x + 3y) dx + x² dy = 0 9. 3x 3…

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

Q: . dy Solve if y = (sin x)*, for 0 <x <; dx dy (sin x)*[x cot x + In(sin x)] dy (sin x)*(x cos x +…

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A: We have to write the right side of trigonometric  identity.

Q: 8. dr+ (2r cot 0 + sin 20) d0 = 0.

A: This will be a linear differential equation of r. We will write this in standard form and then solve…

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A: If y=tan-1cos x, then we have to find dydx.

Q: x cos x Y = sin* cOS x find d dx | sin-

A: To  find: dydx=?

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A: ddxx3+3Apply chain rule:=12x3+3ddxx3+3=12x3+3· 3x2Simplify:=3x22x3+3

Q: f(t) = 3 sinh 2t + 3 sin 2t ; L{f(t)} =?

A: The given function is f(t)=3 sinh 2t+3 sin 2t. The following formulae are used in finding the…

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A: x =∫dx5-3x Let 5-3x = U ⇒-3dx=du = dx =-1/3 du   So,  I = ∫1/u   (-1/3 du) = -1/3 ln u+c = -1/3 ln…

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Q: .L.H.S.-R.H.S. HW/ Brove that: (1) 1-tan? x=sechx (2) coth x-1=csch?x (3) sinh¢cFy)=sinhx.coshy…

A: As per our guidelines we need to solve only 3 questions.please,repost the remaining questions as…

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Q: QI: Find dy/dx for the following 1. y = (sin x + cos x) sec x 2. y 3. Y= (2 -x) tan2 x sinx+ cosx…

A: Product rule of differentiation:     ddx(f.g)=fg' + gf'

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A: % Matlab script to create 2 subplots (mesh and surf) % create the matrices X, Y both between…

Q: e* +e* cosh(x) = cosh(0) = ? 33- e* -e sinh(x) = → sinh(0) = ? 2

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A: Find your answer below

Q: FIND dy/dx for the following Question sin x.cos x 1+2.In x 3 y cot x (ans.: 4 tan x 2 27) 2 x(1+ 2…

A: Given: y43=sinx cosx1+2ln x   ...(1)To find : dydx=?Formula: sin 2x=2sin x cos xcos 2x =cos2 x-sin2…

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A: Use the concept of derivative of an Antiderivative.

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A: given,

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A: b) we know that  ddx∫f(x)g(x)H(t)dt=[H(g(x)g'(x))-H(f(x)f'(x))] we have ∫xsin(x)t2+1dt…

Q: d²y dy + 2y sin? x = e-cos * sin² x dx Solve : + (3 sin x – cot x) dx?

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Q: 9) S 2 cot 2x cos x dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: dy Solve if y = (sin x)*, for 0 < x <. dx dy (sin x)* cot x dy (sin x)*[x cot x + In(sin x)] dx dx…

A: Gg

Q: cos x -dx = sin x O A. In 3 В. In e C. In 2 D. In 4 B.

A: