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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integrals. 3 (x + 1)² dx…

A: See the details solution in the details

Q: Verify the value of the definite integral, where n is a positive integer.

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Q: sec 0 tan 0 cos(sec 0) d0

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Q: Find the following indefinite integrals. (i) (ii) | cos (2x) sin (2xr) dx

A: According to question  given :(i) ∫xex21+ex2dx(ii) ∫cos3(2x) sin2(2x) dx

Q: Find the indefinite integral of the following function. ncos(6 )dt sin(6t) 6 O cos(6 m) +C 6 sin(6…

A: i) ∫πcos(6 πt)dtii) ∫253u du

Q: Evaluate the definite integral. n/4 sin(t) dt cos²(t) COS

A: We have to find out

Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: Evaluate the indefinite integral: ∫ cos t cos(sin t) dt

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Q: 1. Evaluate the indefinite integral and check your answer by differentiation 6dx a) S (z – /2) b) J…

A: To evaluate the indefinite integral. a)  ∫6 dxx - 23 b) ∫cos2x2 dx

Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)…

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Q: Determine the following definite integrals: (a) (sin(x) + =) d.x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Evaluate the definite integral.

A: Consider the given integral. I=∫-π3π3x4sinx The given function is continuous function in the given…

Q: Evaluate these definite integrals: L, ¢x³ – 3x + 2) dx a. 2e b. S"( cosx – ) dx (Vz – z) dz с.

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Q: Evaluate the indefinite integral sin (t)cos (t)dt

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Q: Evaluate the definite integral. 7 cos(xt/2) dt

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Q: Find the following indefinite integral: ∫ x1/3 sin(x4/3-8) dx

A: Given,            ∫ x13sin(x43-8)dx

Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: Evaluate the definite integral. T/2 esin(x) cos(x)dx

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Q: (T/2 sin*(x) cos (x) dx

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Q: Evaluate the following integrals and check by differentiation: 1. J cos 4 x dx. 2. J 5 sec2 2x dx.…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Find the following definite integral where A is a constant and A > 2: | (10z + 17z +1) dx = %3D

A: We have to find the integral of∫2A(10x3+17x+1)dx, where A>2. Applying the sum rule of…

Q: Evaluate the definite integral. e sin (t) dt %3D

A:

Q: 6. Evaluate the following definite integral using the fact that sin x dx = 1. S. | (2 sin x + 3) dx

A: ∫0π2(2sinx+3)dx Take integral for each term ∫0π2(2sinx+3)dx∫0π22sinx dx+∫0π23 dx2∫0π2sinxdx+3∫0π2dx…

Q: TT sinx sin 2x dx 2 cos x

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Q: Evaluate the definite integral. cos(x)dx

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Q: Evaluate the definite integral T 8 sin(x)da

A:

Q: Determine the indefinite integral e - e¯ª cos x dx.

A: ∫e-xcosx dx

Q: Evaluate the definite integral. * T/2 9 cos(x) sin(sin(x)) dx

A:

Q: Evaluate the definite integral. 5 sin (z) cos(x)dx 0.

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

Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Evaluate the definite integral on the interval [0, pi/4] sin(t) / cos^2(t)  dt

A: By substitution, we calculate the value of given integral.

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: Evaluate the following definite integrals.

A: I =  ∫01xsinπx.dx  ................(1)we know ∫abf(x).dx = ∫abf(a+b-x).dx

Q: Find the general indefinite integral using definition. (3t*-t3+6t2 b) S(3 sin x – 4e* + 5* + 6) dx -

A: Integration Question

Q: Find the following integral. Note that you can check your answer by differentiation. / (t+ 1)? t2 dt…

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 9 cos x dx = J…

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Q: Determine the following indefinite integral. Use C to represent an arbitrary constant. / (sec2 (x) –…

A: The detailed solution is given below Thank you

Q: evaluate the following definite integral : , π/2 3 sinx cos x dx let u = 1 + 3 sin? x 1 + 3sin?,

A: Given,         ∫0π23sinxcosx1+3sin2xdx ;  Let u=1+3sin2x

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 | cos(e) – 1 de 2(1+ cos…

A: NOTE: Refresh your page if you can't see any equations. . ..................(1) take  using…

Q: 2. Use the substitution method to determine the following indefinite integrals: (a) / cos(2r) dæ (b)…

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Q: Evaluate the indefinite integral.

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Q: Evaluate the definite integral. 4 cos(xt/2) dt

A: We need to evaluate the following integral. So,            ∫014cosπt2dt=4·∫01cosπt2dtLet…

Q: Evaluate the definite integral. cos(Tx) dx 0.

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Q: Refer to the definite integral to answer the following questions: 4 [*(16-x²) dx

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Evaluate the definite integral 15 cos(t)dt:

A:

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

Q: 3. Evaluate the following definite integrals using a change of variables. a. F sin(2x) dx b. [x Vx+1…

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Q: cos“(x) sin(x)dx

A: See attached file for a step by step explanation to find the given integral.

Q: Evaluate the following indefinite integral | 8 sin(x) – 2 cos(x) dx =

A: We have to find integral