Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x – x²) dx xpS (9 -п/2 c) S" csc? 0 dO In/4 d) S,*(x – 1)(3x + 2) dx T/4 1+cos² 0 d0 cos² 0 e)

Q: Exercise 9: Use the above out-lined substitution of u = tan(x/2) to solve the integral: cos(x) J…

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

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Q: cos®xdx CoS Xx, 0.

A: We have to evaluate the integral.

Q: F(4) = [, * G&+2) dt (3t +2) dt

A: Consider  F(x)=∫2x+2(3t+2)dt

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.

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Q: In Exercises 1–8, decide whether the integral is improper. Explain your reasoning. dx dx 1. 5х — 3 -…

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Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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

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Q: Use the substitution formula to evaluate the integrals ∫ pi over 4 at the top and 0 at the bottom…

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Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. V3 2 8 dx V1-x?

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Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: (8 sin x) dx. Noto: Round…

A: Our Aim is to evaluate the integral given below:-∫π/4π/3 (8 sin x) dx -(i) using Fundamental Theorem…

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫e3x + 1 dx

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Q: Use the fundamental theorem of calculus to evaluate the following definite integral. | (3x2 + 9) dx…

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

Q: Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6-…

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Q: Evaluate the integral. ∫0 π/4 tan4 t dt

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Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 4t-5 dt. If the integral does not…

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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: The integral of the right hand member of the first order LDE +2r cote = sin20 is: de -cos4e + C A 2…

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Q: Use the Fundamental Theorem of Calculus to evaluate the integral: 5/4 sin x dx. Jπ/2 C. A. - B. D.…

A: The objective of the question is evaluate definite integral using the fundamental theorem and choose…

Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: Use Part II of the Fundamental Theorem of Calculus to evaluate the integral. So (cx³ + dx² + e) dx…

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Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 3 | 4x(1 – x² )dx = -1 i…

A: Given that: ∫-134x(1-x2)dx

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

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Q: Evaluate the definite integral using the Fundamental Theorem of Calculus. 7/4 (8 sin(x) + 2 cos(2x))…

A: To evaluate the definite integral using fundamental theorem of calculus.

Q: Evaluate the following integral using the Fundamental Theorem of Calculus. 1/2 | (cos x- 4) dx -1/2…

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Q: Find the indefinite integral.

A: Given : ∫tan2tt2dt

Q: The suitable substitution to evaluate the integral cos (2x) dx is csc (2x) none O u= Cos(2x) O u=…

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Q: Use the Fundamental Theorem to evaluate the definite integral exactly. | (sint + cos t) dt %3D

A: We have to solve the problem

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: | (6+xvF)dx

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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: Evaluate the following definite integral using the Fundamental Theorem 1 of Calculus: 5+ dx x²

A: NOTE: Refresh your page if you can't see any equations. .

Q: 1 -) Prove the existence of the improper integral 1 (In x) sin – dx -

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Q: Let G(x) = tan 9t dt. In order to use the Fundamental Theorem of Calculus (Part 2), G(x) needs to be…

A: Let a,b>0 with b>a Then we can write, ∫abf(x) dx as ∫0bf(x) dx - ∫0af(x)dx

Q: Evaluate the integral / 'cos(æ – In x) dx dy.

A: We need to change the order of double integral

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 | 4x(1 – x² )dx = -1 i

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Q: Evaluate the integral 3. 2х cos(xy)dydx 2

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Q: Evaluate the integral: f/2² sin (-) dt du ,2

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Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 | 4x(1 – x*)dx = i -1

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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: 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…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A: The given integral,    ∫3x2ex3dx

Q: In (x le) (2– sec²x)elmtafcsec?x sec(3A – x) - dx to be integrable using the formula 'du? What…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.