Evaluate each integral by interpreting it in terms of areas. 4 (а) f(x) dx '10 (b) f(x) dx '14 f(x) dx 10 (c)

Q: 1. Evaluate the integral using integration by parts 75/2 In x dx

A: The formula for integration by parts is Let, That implies,

Q: Evaluate the integral.

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Q: Evaluate the integrals ∫(ln x)-3/x dx

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Q: x3 . In x dx

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Q: In V3 dx 1+e2cx

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Q: do a double integral where x ranges from 0 to 1/2 and y ranges from 1/4 to 1/2

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Q: Evaluate the integral using tabular integration by parts. (3 x² – x + 1) e¬¤ dæ +C -

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: Evaluate the integrals in ∫x(ln 2)-1 dx

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Q: |x| dx 1 X V1– x² -1

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Q: Evaluate the integrals in ln ∫(ln x)/x ln x dx

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Q: Evaluate the integral. inegral  0 to 1    [ (x-4) / ( x2  - 5 x +6 )] dx

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Q: Evaluate the integral In(x) le2 x[ln4(x)-1] e3

A: The integration of the integral is  ln(x)/[x(ln4x -1)] limit from e2 to e3.

Q: Evaluate the integral dx et – e-x

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Q: Evaluate the given integral. Use integration by parts 4x' In(5x)dx

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Q: evaluate the integral (In (X )Ć dx X3

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Q: dx Evaluate the improper integral if it exists

A: The solution is given as follows

Q: x e* dx (1+х)2

A: Explanation of the answer is as follows

Q: Evaluate the integral using integration by parts 2x e 5x

A: I=∫uv.dv=u∫vdv-∫du∫vdv where u is first function and v is second function

Q: 2 -y2 dydx e 0. 2x

A: The answer is given as follows:

Q: Evaluate the integrals in ∫ln x dx/x√(ln2 x + 1)

A: Consider the following integral: ∫lnxxln2x+1dx=I Substitute ln2x+1=u→2lnxxdx=du in the above…

Q: In x dx

A: The given integral is ∫-11lnxdx  If f(x) is continuous on [a, ∞) then the improper integral is…

Q: Evaluate the integral from [1, e^3] ln^3(x^2) / x  dx

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Q: Evaluate the integrals ∫ ln x/x3 dx

A: Evaluate the integrals  ∫lnxx3dx

Q: Approximate the integral from 1 to -3 of e-x dx using four equal subintervals.

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Q: 4. f In (2x + 1) dx =

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Q: 1. Evaluate the integral using integration by parts where possible. Z2 x In(8x)dx

A: we  have ∫12x*ln(8x) dx   we have to apply integration by parts ∫u v dx = u∫v dx −∫u' (∫v dx) dx…

Q: If f(x)dx - + what are the bounds of integration for the first integral? a = and %3D

A: To find the bounds of integration

Q: x Inx dx

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Q: Evaluate the integral using integration by parts x2 In (x)dx 1

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Q: Evaluate the integral: S (in ce) dx = (8 ln(x))²dx 2 (x8) ( ×

A: Evaluate ∫lnx82dx=?

Q: Evaluate the integrals ∫ ln x/x2 dx

A: Evaluate the integral ∫lnxx2dx.

Q: dx -x - e

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Q: | x²ln(x) dx 1

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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: Evaluate the definite integral using integration by parts.

A: Recall the following fact.

Q: Determine the value of the integral: integral sign:  (x^2)(e^-x^3)

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Q: 1. Evaluate (2 – x) dx by drawing a picture and interpreting the integral in terms of areas.

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Q: In x - dx

A: Given integral,           ∫eelnxx2dx

Q: Evaluate the integral using tabular integration by parts. (2 x² – x +3) e +C -

A: We can evaluate the given integral by the tabular integration by parts method.

Q: Evaluate the integrals in ∫(ln x)3/2x dx

A: Consider the given integral, ∫lnx32xdx use the substitution, t=lnxx=etdx=etdt so, the integral…

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: Evaluate the improper integral. x In6x dx 0.

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Q: + 3x dz. x2 + 1

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Q: Evaluate the integral. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: Evaluate the integral.  integral   csc x  dx

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Q: Evaluate the integrals ∫tan (ln y)/y dy

A: Given ∫tan(ln(y))ydy

Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: 3. x+1 dx

A: let I=∫5x32x+1dxput 2x+1=u2x=u-1x=(u-1)2and  2x+1=udifferentiate w.r.t.…