3. Use the Fundamental Theorem of Calculus Part 2 to evaluate the integral, or state why the integral may not exist. a) S (u + 3)(u – 1) du b) S (3 sin(x) + e*)dx

Q: Evaluate the following integral using the Fundamental Theorem of Calculus.

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Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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

A: Consider  F(x)=∫2x+2(3t+2)dt

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

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

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Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

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

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

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Q: 3. Use a triple integral to derive the formula f *+ + = 1. = 1.

A: Given: To derive the formula for the volume of the ellipsoid by using a triple integral. x2a2…

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A: The integration of the integral is exsinx.

Q: Evaluate the integral.  integral  t 2 sin 2  t dt

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Q: Evaluate the integrals. Show all work. 1. 0 cos (T0) de 1/2

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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: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: 2. Evaluate the Integrals using the Fundamental Theorem of Calculus. 1. S/4 cos x dx π/4 2. ¹₁ sec²…

A: First I have written the Fundamental theorem of Calculus, using it for given integral and find its…

Q: 3.2. Prove directly from the definition of Itô integrals that t t | B?dB, = B - | B,ds .

A: The answer is given below

Q: The evaluation of the Integral of Sx sinx cosx dx is ) 글x stm2x-x+금stn2x + c (i) x sin'x -x + sin2x…

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Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: Next, integrate with respect to 0. T/2 1 e4 1 - de = 1. | T/2 1 - e4 Again, apply the Fundamental…

A: Here, all the parts are correct except part 3 of 6. The part 3 of 6 is: Evaluate: 12∫0π21-1e4dθ

Q: Evaluate the integral / (6+ sin t)" cos t dt using the substitution u = 6+ sin t. %3D (6+ sin t)ª…

A: Given: ∫6+sint11cost dt To find: ∫6+sint11cost dt using the substitution u=6+sint

Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: 0; x 0

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Q: Evaluate the integral (1+ sin t)' cos t dt using the substitution u = 1+ sin t. (1+ sin t)' cos t dt…

A: Recall: ∫xndx=xn+1n+1+C

Q: b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 2 i) S 4x(1 – x³)dx…

A: (i). ∫-124x1-x2dx The antiderivative of 4x1-x2 or 4x-4x3 is 2x2-x4 Therefore,…

Q: b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 2. L, 4x(1 – x²)dx…

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Q: Use the Fundamental Theorem of Line Integrals to calculate d exactly. 7-7+4y²f arqund the top of the…

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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.…

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Q: f (x) = = cos 2x; [0,T] G and

A: topic - mean value theorem

Q: tan (in |4x2|) dx is bin sec (In |(2x)ªl)| + C. what is ba The integral of A B) 4 © 1 1

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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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: 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 (if it exists) where If the integral does not…

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Q: Evaluate the integral e'sin e) dx 1- In 2 2 u +3 u + C + C +C cos(e") + C COS -2*+2x + C 21 21

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

A: To find the value of given integral.

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: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: Q.1 Evaluate the given integrals using part I of the Fundamental Theorem of Calculus. [3 Marks] i.…

A: You need to find the integral of the given functions using the fundamental theorem of integration.

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

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Q: Use symmetry to evaluate the double integral. 10 sin(x) dA, R = [0, 2n] × [0, 21]

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: Evaluate the integral.   The integral from 1 to 4 of e^(4/x)/x^2dx

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3…

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 2 | 4x(1 – x² )dx = i -1

A: Given,    ∫-124x(1-x2)dx

Q: Apply Green’s Theorem to evaluate the integrals ∮(3y dx + 2x dy)C: The boundary of 0≤ x ≤π, 0 ≤ y ≤…

A: According to Green's theorem - ∮Pdx+Qdy = ∬D dQdx-dPdydxdy          ...............(1)Given integral…