x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

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Q: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

Q: Evaluate the integral ∫sin5 x/3 cos x/3 dx

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Q: Evaluate the integral.  integral sin 9  x cos 3x dx

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Q: Q2 : Evaluate the integral sin x dx 1-sin² x

A: To find the integrations.

Q: Find the definite integral.

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Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

Q: Evaluate the integrals

A: We have to evaluate the integral;  13) ∫ln4ln9ex/2 dx14) ∫tanxln(cosx) dx

Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: 2. Evaluate the integral: | sinh x cosh² x dx

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Q: d Prove that 1 da (sin-1æ) = V1 – a? -

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Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Compute integral. sin(x) cos(x)V4+sin? (x) dx. 2.

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Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: sin x dx V2-cos² x

A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: Evaluate the integral. sin(5.x) sin(4x) dx

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Q: Evaluate the integral sin'7 x cos x dx

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: ( sin (In 2x) - cos (in 2x))? +x dx 2x

A: Let's find.

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: 2. Integrate | sin x cos? x dx

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Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: Show that sin x dx=1-cos t (0<x<t<}r).

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Q: Evaluate integral sin^4(x) dx

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Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

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Q: S sin(4 + 5x) cos (5x – 4)dx

A: From the given problem: I=∫sin4+5xcos5x-4dx As we know that the trigonometric identity:…

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Find cos x + sin 2x dx 19. sin x

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Q: Sih X pronf:, sin1x) cosinx)dx Sin (1-h)X

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Q: Evaluate the integral.  integral sin 6  x cos 5x dx

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Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

A:

Q: TC 4. sin(2x) cos(2x) dx

A: To evaluate the definite integral

Q: Evaluate the definite integral. 1 2 sin-'(x) dx /1 – x²

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Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Find the indefinite integral ∫ sin x/(1 + cos x)   dx

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Q: 2T COs x dx

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Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

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Q: Evaluate sin integral (4x) cos(5x) dx

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: dx |2 sin 2 sin x — сoS X

A: I have appended the formula used in the solution part

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

Q: Evaluate the integral. 2 sin -1 x dx

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Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: a. dx 1+ sin(ax)

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Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx