Use the substitution formula to evaluate the integrals ∫ pi over 4 at the top and 0 at the bottom (1+sin2t) co2t dt and ∫pi over 2 at the top and pi over 4 at the bottom (1+sin2t) cos2t dt

Q: Write the integral in terms of u and du. Then evaluate:                                       ∫…

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Q: Evaluate the integrals.∫cos 7w/(16 + sin2 7w)dw

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Q: Evaluate the indefinite integral. asin (a)cos(2)dz: + C %3D

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Q: 5tan 2x -dx sin²2x-1 8.

A: Put tan2x=t and using integration of ax dx =ax /loga

Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C…

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Q: Use the substitution t = tan(x/2) to transform the integrand into a rational function of t and then…

A: Let  I = ∫0π2 5 sin 2x 2 + cos x   dx

Q: Evaluate the integrals

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Q: Calculate the integral of y = 11 cos (8x) from 0 to Answer = Number Leave your answer in exact form…

A: on solving this we get the

Q: 2n do 3 + sin 0 + cos 0

A: Given integral is ∫02πdθ3+sinθ+cosθ Given z=eiθ We know that  eiθ=cosθ+isinθ e-iθ=cosθ-isinθ So…

Q: Which of the following is equal to sec 2 x tan³x dx to obtain the correct indef inite integral?

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Q: I know it’s u-sub, but I forgot how...

A: Given information:The given integral is

Q: 6z* cos (r*) dr-

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Q: Find the integral t5 cos |dt using the substitution u = t6. Enclose arguments of functions in…

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Q: The suitable substitution to evaluate the integral V tan (2x) dx is cos (2x) COS

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin 2x cos 3x dx

A: given: the integral is:∫sin2xcos3x dx let the given integral ∫sin2xcos3x dx be I. as we know that,…

Q: [ sin³(2x) dx

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Q: Use thě substitution a = 7 tan(0) to evaluate the indefinite integral 40dx x²Væ² + 49 +C

A: Substitute x=7tanθ After differentiating, dx=7sec2θdθ

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: 4 sin320 cos20 d0

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Q: The resulting integral of sin -cos-sino de has the form -F(0)+C- What should be the value of e to…

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Q: Ssin( /3x)cos(-2r)dx

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Q: a) Evaluate the integrals using appropriate substitutions. Sine ii) S de Cos0+1

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Q: Evaluate the integral. A/2 sin!'(0) cos (0) de COS Jo

A: Given : ∫0π2sin11(θ)cos5(θ)dθ ∫0π2sin10(θ)sin(θ)cos5(θ)dθ∫0π2sin2(θ)5sin(θ)cos5(θ)dθwe know that…

Q: Evaluate the integral: 2T So cos² (0)d0 *Input answer as decimal round-off to 2 decimal places

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Q: Evaluate the integral. xp- sin? 3x 15) -In |sin 3x|+ C B) - 1x cot 3x +1 In |sin 3x| + C 3 A)1x cot…

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Q: Evaluate the integrals below: 2 cos2x а) sin2x. [In(sin2x)]? + sin2x .dx, b) хе^.dy

A: We have to evaluate the following integrals,

Q: Evaluate the integrals ∫sin2 2θ cos3 2θ dθ

A: Given:∫ sin22θ cos32θ dθ

Q: Evaluate the indefinite integral. | cos(8z) /4 – sin(8z) da = +C.

A: Let I is the value of given Integral

Q: cos (78) dx, u=7

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Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: 9. | cos (2r) dt

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Q: 2. sin xcos³xdx

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Q: evaluate the integral (Usec. af nitegratun) for the constant बदेशव 1ehan) 5x cos (8x) dx

A: Given

Q: In evaluating / *sin³(2x)cos(2x) dr by substitution, if u = sin(2x) then what will be the resulting…

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Q: Evaluate the integrals ∫7 cos7 t dt

A: We have to evaluate the integral: ∫7 cos 7t dt Solving by substitution method, Assuming, z=7t…

Q: Q1: Evaluate the folowing integrals by using a substitution to reduce it to जकंन standard form: (i)…

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Q: de 1 + sin 0

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Q: In evaluating/ *sin³(2x)cos(2x) dr by substitution, if M = sin(2x) then what will be the resulting…

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral…

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Q: Use the convolution theorem to evaluate the integral. sin(2 · 7) cos((t – T))dr COS

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Q: solve both without using the table of integrals. Q1) integral of cos4xdx   Q2) integral of tan5xdx

A: according to our guidelines we’ll answer the first question since the exact one wasn’t specified.…

Q: Evaluate the integral. TO 9t sin(7t) dt

A: Given query is to find the value of the integral.

Q: Evaluate the integral. cos-1(x) d.

A: We have to evaluate I=∫cos-1(x)dx

Q: Use the substitution formula to evaluate the integral. 1 dx 0 19-x2 O A. 3 cos 1 1 O B. sin O C. sin…

A: You just need to substitute x = 3u and then you will get the standard form.

Q: Use the substitution formula to evaluate the integral. 27 3 cos2 x sin x dx 1/3

A: Given that: ∫π/32π3cos2x.sinxdx

Q: In evaluating | *sin3(2x) cos(2x) dx by substitution, if U = sin( 2x ) then what will be the…

A: First we put sin(2x)=u and then differentiate both sides with respect to x and solve it. 2cos…

Q: Evaluate the indefinite integrals by using the given substitutions to reduce the integrals to…

A: SOLUTION-

Q: Evaluate the integral: 2² sin (²) dt du

A: To evaluate the integral: ∫π2π∫0u2sintudt du

Q: Evaluate the integral from 0 to pi/4: ∫tan4t dt

A: here we use trigonometric identity  tan2x=sec2x-1 and, integration from 0 to π4