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+ Express numbers in exact form. Use symbolic notation and fractions where needed.) g(t) dt = / 8(1) dt =

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A: Since, this is a multiple question according to the Bartleby Answering rule, only first question and…

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Q: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

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

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Q: Find the quadratic approximation of f at x = 0 f(x) = sin In (3x + 1) O A. Q(x) = 1 + 3x + 5x 9 B.…

A: The given function is: fx=sin ln3x+1 To find the quadratic approximation of f at x=0

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

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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

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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: 16 – x2 dx - Evaluate the integral: 9x?

A: (A)  x=4sin(θ) (B)  19cot2(θ) (C)  -19θ-19cot(θ) (D)  -19arcsin14x-16-x29x

Q: / 2) + (2 / √x)) dx 2. ∫ ((t√t + √t) / t2) dt

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

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

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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: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: Which of the following integration expression can be transformed into integral of power 2 dx (A)…

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

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Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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

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Q: Find the indefinite integral.

A: Consider the given integral ∫2-1tt2dt

Q: Find the indefinite integral. a. -+c -7x + C e а. 1 b. -7x + C 7x 1 -7x - +C с. 7 d. -7e-1x + C e.…

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Q: Use residue theory to calculate the following integrals: 3x 1. Loo (x² + 49) (x² − 2x+5) (a) P.V. dx

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Evaluate the integral analytically. 1 е бх 1+ e 6x

A: consider I= ∫01e6x1=e6xdx

Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Which of the following integration expression can't be transformed into integral of power 2dx A 4+3x…

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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

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Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: Find the indefinite integral: (t3/2 + t-1/2 - 10t-1) dt

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Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

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

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Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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Q: Find the quadratic approximation of f at x = 0. f(x) = In (1 + sin 7x) 49 O A. Q(x) = 1 + 7x + 7x 49…

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Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

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Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below

Q: Find the indefinite integral. -6w ſe " sin2w dw 3sin2w+cos2w-ów 20 sin2w- 3cos2w +C 20 -sin2w-…

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