-. The integral x+1 dx can be evaluated using the substitution u = x'+ ax +1 once. Determine a and x' +ax + 1 evaluate the integral. Show the work that leads to your answer.

Q: Find a bound for the error in the approximation M10 to the given integral (but do not calculate…

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Q: e2x dx 10. V1+e2x

A:

Q: Find the indefinite integral.

A: We have to evaluate the following integral: ∫x2-3x+2x+1dx

Q: Find the indefinite integral.

A: Given : The indefinite integral is ∫ 17x -2 dx .

Q: 1 d.x x In x i)

A:

Q: 2 3x dx xp, Evaluate the indefinite integral.

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Q: dz 2+2vz

A: The given integral,       ∫dz2+2z

Q: Find the indefinite integral.

A: To evaluate the integral: ∫1x2-4dx Solution: Let substitute x=2secθ. dxdθ=2secθ tanθdx=2secθ tanθ dθ…

Q: Find the indefinite integral using any method.

A: The integral to be solved is . Substitute . Differentiate both sides.

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Evaluate the indefinite integral. dx 2 5x

A: We have to find given integral.

Q: Evaluate the indefinite integral. dx xV 25 – x2 -

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Q: Evaluate the integral. integral    (  x2 + 1 )/ (x-3) (x-2) 3 dx

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Q: | V5x-4 dx

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Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: Evaluate the improper integral. If the integral diverges, state so. dx 1. dx 2. (x + 1)² 0.

A: 1.Given, II=∫1∞dxx23As it is an improper integral,we write it as=limt→∞∫1tdxx23=limt→∞∫1tdxx232…

Q: Evaluate the improper integral 1 dx x - 1

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Q: dx (apply the properties on how to solve improper integrals 1 – x²

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

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: Find the indefinite integral.

A: To find: The indefinite integral of ∫1x231+x13dx. Formula used: ∫afxdx=a∫fxdx ∫1xdx=ln x+C

Q: Evaluate the indefinite integral: 3 dx J x In(5x)

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Q: Evaluate the definite integral.

A: ∫15x2x-1 dx Consider, ∫x2x-1 dx Put, 2x-1=t⇒21-0=dtdx⇒2 dx=dt⇒dx=dt2 Therefore, ∫x2x-1 dx=∫t+12tdt2…

Q: Find the indefinite integral. X< + 12x + 1 .3 dx to x° + 18x² + 3x + 4 ,2

A: Given: Let I=∫x2+12x+1x3+18x2+3x+4 dx To Find: To evaluate the given indefinite integral.

Q: Find the indefinite integral ∫(1/x2−1x3)dx.

A: Given Data The integral function is ꭍ(1/x²-1xᶟ)dx.   Write the integral function in individual…

Q: Evaluate the indefinite integral. V 4 + x² dx = %D

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Q: 3x2 + 2x +1 dx x2

A: See the attachment

Q: Evaluate the integral

A: The integral is given by,

Q: Evaluate the integrals.∫x2 cos x3 dx

A: We have  I=∫x2cosx3 dx                          ⋯⋯(1)   Let  x3=t3x2du=dtx2du=dt3 put in equation…

Q: Find the integral: 2 1 Integral 1 to 2   (1 divided by x - 1) dx

A:

Q: Find the indefinite integral 3x2 dx et 2.

A: ∫ex-3x22 dx

Q: Evaluate the indefinite integral

A: Given:

Q: Compute the indefinite integral 2. 4e2a + 6x 5) dx. - -

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Q: evaluate the indefinite integral dx/((16+x^2)^2)

A: Use the fomula to simplify the integral .

Q: Find the general indefinite integral.   ∫ (x2+  x-2)    dx

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Q: [(2x-1)"dx

A: Here we have to find the given value of the integration: ∫2x−110dx

Q: (1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

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Q: | (3x² + 4x + 1) dx

A: The power rule of integral is,

Q: Find the indefinite integral ∫ (5 − ex) / e2x dx

A: We have find indefinite integral: ∫5-exe2xdx Separating each terms of the rational function of the…

Q: Find the integral 15 x+3 √1-x² dx

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Q: dx (4 + x²)²

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Q: Evaluate the definite integral. integral 0 to 1  ( x divided by 1+2x2) dx

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Q: Evaluate the indefinite integral 6 dx %| x2 Vx2 + 9

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Q: Find the indefinite integral. 1 Js (12x) dx 3+ 2x

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Q: Evaluate the indefinite integral dx x(x²+2x+1)

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Q: 3 aluate the indefinite integral by using the substitution u = x + x° to reduce integral to standard…

A: Please refer to the image below

Q: 1. Find the exact value of the iterated integral by changing the order of the integration: 8 2 1…

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Q: Find the general indefinite integral.   ∫ (√ x3+  3√ x2)    dx

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Q: * (x² + 4)³/2 -dx

A: Find the integral of the give function: ∫x2+432xdx

Q: dx V5 + 4x – x²

A: Integrate

Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

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.