Evaluate the integrals SE rln(r² + 1)drd0 =? a) Оpi/4 b) O pi/2 c) O 2pi d) O pi O Boş bırak 2-

Q: 4) Compute the integral where is the closed chrve SRe (z²)dz -2

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Q: Find the product of the integral 1- LL,x? e*ydxdy

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Q: Evaluate the integral

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Q: Use the substitution formula to evaluate the integral 6r dr V16• 3r² O 2V19 -8 O NIS .4

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Q: Evaluate the integral by interpreting it in terms of areas. 8 64 – x2 dx 8

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Q: Evaluate the integral, 12 sec(4t) dt 2+3 tan (4t) dt = 2+3 tan (4t)

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Q: 2. Use the form of the definition of the integral given in Theorem 4 (p. 380) to evaluate the…

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Q: Write the integral in terms of u and du. Then evaluate. |IV21? + 11 dr, u = 21² + 1 - 2t? + 11

A: Given,            ∫t2t2+11dt

Q: Evaluate the double integral : ľ (o – 162) de dy

A: In the question it is asked to calculate the value of double integral…

Q: Compute the integral based on 2where g is the cloed cuve 2.

A: In this question, we find the value of complex integral    I=∫γ z-2dz For the given contour.

Q: Evaluate the integral using FTC I.

A: The given integral is ∫-32 u2 du. It is known that ∫ u2 du =u33+C.

Q: Evaluate the integral. | (In(3:2))° de +C %3D

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Q: Evaluate the integral by interpreting it in terms of areas:

A: The given integral is

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integrals in Exercises

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: tVt2 + 2dt.

A: we can evaluate  the given integral by substitution method(Substitute  u=t²+2).

Q: n. b) 2e u+2 dydz. 0 Ji

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Q: Evaluate the integral by interpreting it in terms of areas: | (4 + 32) dz : %3D

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Q: Evaluate the indefinite integral ∫⟨4cos2t,4tet2,2t+3t2⟩dt.

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Q: Find the anc length oF t1x)=x° on [o,] Hint; use the Integral Tables,

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Q: Evaluate the integral. In 4 In 3 In 4 dx%3D In 3

A: The value of the given integral is 1.

Q: evaluate the integral using the methods covered in the text so far.

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Q: Evaluate the integral * cosh? dx -In 2

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Q: 2. Use Cauchy's Integral formula, Evaluate the foll D I - & tantz Z² C: 171=1

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Q: Use Cauchy's Integral formula, Evalnate the following zl=3 • I = 6 %3D 근 (2-21)2

A: Cauchy Integral formula: If f(z) is a analytic function within and on a closed contour C, and if a…

Q: 19. z?e-l/? (a) |z| = 5 %3D

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Q: Evaluate the integral: /25 – z z²dz

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Q: 15. Evaluate the integral zVx² + y²dzdxdy by using cylindirical coordinates.

A: I have Provided this answer in step-2.

Q: Evaluate the integral using FTC I.

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Q: "(2 - sinoy de

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Q: O Evalu ake I dx

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Q: Evaluate the integrals in Exercises 45. tanh dx 46. coth de

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

Q: Compute the given improper integral. Enter the exact value of the answer. 7 In(4x)dr 0,

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Q: Evaluate the integrals ∫8 cot4 t dt

A: The given indefinite integral is: ∫8 cot4t dt Since 8 is a constant, so take it outside. ∫8 cot4t…

Q: Evaluate the integral by interpreting it in terms of areas. 4 + 9 — х2) dx -3

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Q: e that ZIval = iatbisla,bez3 is an integral doncain

A: We have to prove given result:

Q: Evaluate the integral. Snip

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Q: xdx 3 —х

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Q: Evaluate the integral using FTC I.

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Q: So I need to keep the 4 and the cubed in the integral??

A: Yes, you have missed the "4" and the cube.

Q: In 4 et dt Ve2t+81

A: Integration is much complicated because of the limits. Without limits, look at the substitution.

Q: Evaluate the integral by interpreting it in terms of areas. 3 + v9 - x2) dx

A: According to the given information it is required to interpret the integral in terms of area.

Q: Evaluate the integral: (In z)6 dz %3D

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Q: Evaluate the integral * » In 4 coth x dx In 2

A: In this question we have to solve this integral.

Q: Evaluate the integral. (Re du |u3- u?

A: Solution is written in below steps.

Q: Evaluate the integral over the rectangle R: (a) |/ ev dA, 0 < ¤ < In 2, 0 < y < In 2 R (b) dA, 0 < x…

A: As we know that; The Power rule; ∫xndx=xn+1n+1+C ; n≠-1 And ∫eax+bdx=1aeax+b+C   (a). Given:…

Q: Calculate the integral ∞∫0dxx2+16.

A: These are called improper integrals so in this case,…

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral. 81 In y 64 Vy

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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.