2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

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Q: Evaluate the integral. 16 In(y) dy Vy

A:

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: What is the integral of f(x) within the interval [2, 4]? AY 6- O Area = 2.0 O Area = 2.5 O Area =…

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Q: 1 de is not an improper integral x +1

A:

Q: Evaluate the itorated integral. 24 ,xty *ty dx dy

A: First we need to calculate integral with respect to x then y

Q: e2 In(x) da

A:

Q: Evaluate the iterated integral. In 4 In 3 e 2x+Y dy dx 0 1 In 4 In 3 | | e 2x+ydy | dx = 0 1 (Type…

A: Solve the following integral

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: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

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Q: Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by…

A: greens theorem

Q: Consider the integral 3 dx V1 – x² If the integral is divergent, type an upper-case "D". Otherwise,…

A:

Q: Evaluate the iterated integral. In 4 In3 2x+Y dy dx 0 1 **y In 4 In 3 e2x + Y dy dx = 0 1 (Type an…

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Q: evaluate the iterated integral.

A: ∫12∫042xydydx

Q: Apply Cauchy integral formula to find the value of the integral ſ. AG-DE dz; where C: |z| = 3. 2z-1

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Q: Evaluate the iterated integral: e dydx

A:

Q: Compute the following integrals (a) Sial dz. Iz%31 z2+z+2

A: Take fz=1z2+z+2 Equating the denominator to 0, we get z2+z+2=0⇒z--1+7i2z--1-7i2=0 Hence…

Q: Evaluate the improper integral A 0 B (C) 2 9 mit 3 4 √1²23 3³/30 D) diverges dx

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Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: Evaluate the integral . In 3 S. Jo Cery) dy dx In4

A:

Q: DEvaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x 2. %3D

A: Integration of cos(x) = sin(x) Integration of sin(x) = -cos(x)

Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

A:

Q: Evaluate the improper integral 1). Sa -2* 2 dx x2-2x

A: Given: ∫3∞2x2-2xdx We have to evaluate the improper integral.

Q: Use simpson's 1/3 rules with n=8 to evaluate the integral of lower limit 1 and upper limit 5…

A:

Q: Evaluate the integral of sinº x dx from o to n/2. А. П/32 В. гп/17 С. зп/32 D. 5n/32

A: We know, 2sin2A=1−cos2A  2cos2A=1+cos2A2cosAcosB=cos(A+B)+cos(A−B)

Q: Evaluate the improper integral dx (5 – x)³ K MANUSIA KERANA T

A: Recall: Improper Integral:      If f(x) is continuous on the interval [a,b) and not continuous at…

Q: Evaluate the integral 'In (Inz) dz X

A: Note: instead of x there should be z in denominator otherwise x behave likes constant.

Q: Evaluate the integrals. In 3 6tei + Te'j+ 2 ln tk dt 18(In(3)-1)i+7(3-e)j+2(In(3))(

A: Topic- integration

Q: 39. Use a software application to compute the integrals у — х dx dy (x + y)³ у — х dy dx Jo (x + y)³…

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Q: Evaluate the iterated integral. In 3 In 5 SS 3x+2y dy dx e 0 1 In 3 In 5 || 3x+2Ydy dx= 0 1 (Type an…

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Q: 3 3y Evaluate the iterated integral ry de dy.

A:

Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x dx

Q: (8) Evaluate the contour integral: 2021 e1/z² dz. Izl=2

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Q: 1+1 dz is 1+ z6 By comparison test, the improper integral

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Q: S(3x – 2)(x + 1) dx

A: First multiply the expression under Integral then integrate and put the limits

Q: 2. Use Cauchy3 Integral formula, Evaluate the following • I=0 e %3D

A: The given problem is to evaluate the given complex integral over the given contour using cauchy…

Q: he integral dx こ [in(x)]? x[In(x

A: Given integral is ∫1x(1nx]2dx let’s find the value

Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: Evaluate the iterated integral. 9. .5 dy dx dz Jo

A: We need to evaluate integral.

Q: Evaluate the iterated integral. In 5 In 3 4x+2y dy dx e 0 1 In 5 In 3 | 4x+2y dy dx = 0 1 (Type an…

A:

Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

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Q: Compute the integral: Integral of (e4x+5ex+2 divided by ex) (dx)

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Q: 9 In evaluating the improper integral , (1- 3x)2 dx ,which of the following is true? 3 A lim 3x B…

A: Given,

Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: Evaluate the iterated integral. In 5 In 2 4x +4y dy dx 0 1 In 5 In 2 4x+ 4y dy dx = *Ydy dx = 0 1

A: Let's find.

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.