Use the figure to evaluate the definite integrals g(t) dt and g(t) dt. y y = g(t) 1 1 2 3 4 -1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) g(t) dt = g(t) dt =

Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

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

Q: Evaluate the integral. бл t2 sin(2t) dt

A: We will apply ILATE rule hence t2 will be first function and sin2t will be second

Q: In(x) Differentiate the function F(x) = | cos(e') dt %3| 1/r Show and justify your work. (Hint:…

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Q: Evaluate the integrals ∫√t sin (2t3/2) dt

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Q: Find the indefinite integral. | t17 dt : +C

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Q: Evaluate the integral •5 sin(t)dt 6.

A: Given:∫65sintdt

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: By the odd extension method applied to the function f (x) = e¯2x, wherex > 0, the Fourier integral…

A: Given the function  fx=e-2x

Q: Evaluate the integral. t2 sin(2t) dt

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Q: Find the indefinite integral. (8ti + j + k) dt + C

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Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

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Q: 8 cos" 2πt dt

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Q: T/3 3 sin (3t) -dt. 5 - cos (3t) Evaluate the integral

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Q: Obtain a formula that expresses the integral ∫cosn x dx

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Q: Find the indefinite integral. -0.02t dt = +C

A: It is given to find out the indefinite integral of f(x)=e-0.02t We know that ∫exdx=ex

Q: Evaluate the definite integral. t(5 – t)² dt

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Q: Find a formula for the function represented by the integral 3t dt

A: Please refer to the image below.

Q: Find the indefinite integral. 3 8 dt = t3 t2 +C

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Q: 17. Consider f(x) = dt. DO NOT state that f(x) = In x but explain how it behaves exactly like the…

A: In the question we need to evaluate the integral.

Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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Q: Use the figure to evaluate the definite integrals g(t) dt and g(t) dt. y y = g(t) 2 1 1 4 -1 -2+…

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Q: In(x) Differentiate the function F(æ) | cos(e') dt (for x>0). %3D 1/r Show and justify your work.…

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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: Find the indefinite integral. t2 dt 3= t3 +C

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Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

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

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Q: Evaluate the integral.

A: The integral ∫0π6tsin2tdt. We have to evaluate the value of this integral.

Q: 1. Use formal substitution to find the indefinite integral (a). de f(-6a) (r-3) de (b)

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Q: Find the indefinite integral. ∫(e1t/t2) dt

A: Given: I=∫e1tt2dt for evaluating given integral, in given integral we substitute  1t=p…

Q: Evaluate the given definite integral using appropriate substitution: dx = 1– 2x A) 8ln(5/3) 2ln(5/3)…

A: From the given integration: I=∫2341-2xdx  ...1 Apply the substitution method to calculate the given…

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

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Q: Evaluate the indefinite integral. dt I (t + 13)8 + C

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Q: Obtain a formula that expresses the integral [cos". cos" x dx

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Q: (8ti + tj – k) dt

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Q: Find the indefinite integral.

A: Given : ∫tan2tt2dt

Q: Find the indefinite integral ∫ t/√(1 − t4) dt

A: Given integral, ∫t1-t4 dt

Q: d Calculate the integral 2r -x

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Q: Evaluate the definite integral. •4 ti + t?j| dt 3 |(7 - 1) 2 17 3 173 3

A: The value of the given integral is 1/3(173/2 - 1)

Q: Find the indefinite integral.

A: Consider the given integral ∫2-1tt2dt

Q: Evaluate the definite integral. 2 St³√₁+t² dt 0

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Q: Evaluate the integral. | Te" cos(2x) de = 7e* cos(2x) dx +C

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Q: Evaluate the integrals ∫cos t/1 - sin t dt

A: Given :           ∫cos t1-sin tdt

Q: Evaluate the integrals

A: Our Aim is to evaluate the integral given below:-∫-π3π3 sin2(t) dt.

Q: Find the indefinite integrals: x5/2 + 4x +1 a) / 2 + Te' ) dt t3 6t +

A: We know that ∫xn dx = xn+1n+1+C         n≠-1 ∫1x dx = lnx+C

Q: Use the figure to evaluate the definite integrals / g g(1) dt and g(1) dt. y = g(1) 2 1 -t 1 2 3 4 5…

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Q: Evaluate the definite integrals a) Vi dt = 16 1 dz = b) 64 / dx = 8.

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Q: i +j- t3/2 k ) dt |

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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: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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Q: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral