Use the Residue to Evaluate the following Improper integral: dx x² – 2x + 2

Q: Evaluate the integral, if it exists.  ∫01 y2 √(y3 + 1) dy

A:

Q: Evaluate the integral by making the given substitution. Sx x +2 dx, u = x³ +2

A: The given integrand is  x2 (x3+2)1/2

Q: |In (x)| dx 00 1+ x2

A: Given integral

Q: Use Romberg integration to compute R33 for the following integral x sin x dx

A: The solution is

Q: Use the Residue to Evaluate the following Improper integral: dx x² + 2x + 2

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Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. La (12…

A: According to the given information, it is required to evaluate the integral.

Q: de V1+4x

A:

Q: Evaluate the integral using the following values. x dx = 60 x dx = 6, dx = 2 J2 %3D 5x dx J2

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Q: Evaluate the integral f 2x (x? + 1)“ dx using the substitution u = x2 + 1.

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Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. dx

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Q: Evaluate the integral by making the given substitution. x-Vx3 + 10 dx, u = x3 + 10

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Q: Evaluate the given integral using the substitution (or method) dx; u = . 7e +C Show My Work…

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Q: Evaluate the integral by making the given substitution.   ∫ x2  √( x3  + 1)    dx , u =  x3   +1

A: The integral formula to be used are: ∫xn dx=xn+1n+1+C, where C is an integral constant. The integral…

Q: - dx 5x² +3 c)

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Q: Evaluate the integral using the given substitution. (Vx cos (x3/2- 4) dx

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Q: Evaluate the following integral by using method of substitution: 1/ (1+9x^2) dx Limit: 0 to 1/√3

A: NOTE: Refresh your page if you can't see any equations. . substitute  ............put it back in…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. dy /2y + 1 +C

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Q: V3 2 dy 1- у?

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Q: Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D". 00…

A: Given integration is, ∫1∞1(6x+1)2dx Let,  6x+1=u⇒6dx=du So, when x=1, u=7 when x=∞, u=∞

Q: Define the following improper integrals integral a to b f(x) dx

A: Let F'(x)=f(x) then,

Q: 7 dx. J 2+ Vx – 4

A:

Q: Compute the integral by algebraic substitution: 7 dx. 2+ Vx – 4

A: Given: ∫72+x-4dx

Q: Evaluate the integral using the given substitution. dx ,u = 6x + 1

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Q: Evaluate the integral with the order reversed. dx dy -2 0

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Q: Evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a:…

A: given,         A=∫x2cosx3+1dx

Q: dx (x + 2)3

A:

Q: dx Væ(x+1)

A: Let I=∫14dxxx+1. Put x=t2 and differentiate it with respect to x. ddxx=ddxt21=2tdtdxdx=2tdt

Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: sin (x²) + C

A:

Q: Use the substitution a 3 sin t to evaluate the integral f V9 – x² dx.

A:

Q: evaluate the integral by making the given substitutions

A: Given,

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Define the following improper integrals integral -1 to 0  f(x) dx

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Q: +00 dx Evaluate the improper integral x(In x)²

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Q: evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

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Q: Find the integral using the substitution u = t3.

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Q: Evaluate the integral, if it exists: lim sinx dx r→+z -r

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integrals: (a)∫xex/2dx (b)∫e2xsinx dx. (c)∫xcos(2x)dx.

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Q: x+1)dx 1. S

A: Let x1/6=ududx=16x5/6du=dx6x5/6

Q: Evaluate the integral f 9(√x² + y²) dxdy.

A:

Q: Q2. Evaluate the iterated integral by changing the order to dx dy. eu dy dx

A: For reversing the integration order, we will replace the limit of x and y with interchangeably. Then…

Q: The improper integral J 1 r2-4x-5 dx is given by:

A: In this question, we reduced the integral into trigonometric form by using suitable transformation.

Q: Define the following improper integrals integral -1 to  1 f(x) dx

A: Given integral is,

Q: (e2x –1)2 dx 1. e 2x

A:

Q: Evaluate the improper integral or show that it diverges: 00 (a) xe dx 7/2 (b) tan x dx

A: a) ∫0∞xe-xdxb) ∫0π2tanx dx

Q: Use the Method of Substitution to find the indefinite integrals: t3et“ dt dx x VIn x

A: The given integral,a) ∫t3 et4 dtb) ∫9xln x4dx

Q: Evaluate the integral.

A: Evaluate the integral.              ∫04-x2x2ydy

Q: and evaluate the Sketch integral reverse 9/x Jy dz

A:

Q: b) r.e dr

A:

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.