Evaluate | VF In(r)dx by using integration by part.

Q: e dy da by reversing the 4-V Evaluate order of integration.

A: Change the limits:

Q: | Va3+1 dx dy 0,

A: ∫01∫y1x3+1dxdy=∫01∫0x2x3+1dydx=∫01x3+1x2-0dx=∫01x2x3+1dx

Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

A: Given ∫8xx+c5dx

Q: Evaluate the integral :(x² + y* )dzc>xcy = ?

A:

Q: ite the integral (Use C for the constant Integration) In Vx)dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dt 1- t10

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Q: Reverse the order of integration I f(x, y)dydx.

A: The limits of integration have a critical role in evaluating a double integral. Usually, the upper…

Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

A:

Q: Change the order of integration and hence evaluate J J² dy dx.

A: Explanation and Solution is given below....

Q: Evaluate the integral. (Use C for the constant of integration.) t dt + 10

A:

Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫t3 e-t2 dt

A: The given integral is Apply substitution method So, the integral is

Q: (x + 2) dx Ja + 4)(x – 2) B) Use the techniques of integration to evaluate

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Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

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Q: Evaluate the following by changing the order of integration: dx dy. z/3

A: Explanation of the solution is given below....

Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: Evaluate the inde integration, SX²J9+x' o

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Q: X' 2 -1 Vx * dx X,

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 5 dx J x(x* + 3)

A: ∫1au+bdu =1alnau+b+C dxndx=nxn-1

Q: Evaluate the integral. (Use C for the constant of integration.) / Incv) In(Vx) dx

A: To evaluate the below integral Simplify it

Q: Use Integration by Parts to compute j x 2 lnx dx, setting u = x 2 anddv = Inxdx.

A: Given integral is ∫x2lnxdx. Consider  u=x2,dv=lnxdxThen du=2xdx.v=xlnx-x

Q: V3 2 dy 1- у?

A:

Q: dt Explain what is wrong with the following integral: |t| VE2 – 1

A: given  I=∫-111tt2-1dt from I  ft=1tt2-1domain of f(t) is t>1,t2-1>0therefore-1<t<1

Q: Use integration by parts to show that | (x) dx = xf(x) –J xf(x) dx

A: For (a), ∫f(x) dx=∫1×f(x) dxBy integration by parts,=∫1 dxf(x)-∫∫1dx×ddxf(x) dx=x f(x)-∫xf'(x) dx

Q: dr 46. First make a substitution, then use integration by parts.

A: Given- ∫x5ex2dx To find the antiderivative first using substitution and then using integration by…

Q: Evaluate the integral. (Use C for the constant of integration.) In(Vx) dx

A: ∫lnxdx=∫lnx12dx=12∫lnxdxLet u=ln(x)du=1xdxdv=dxv=∫dxv=x

Q: Evaluate (r+y)dxdy By Change the order of integration in the integration

A:

Q: Reverse the order of integration in (2xy + 1) dxdy and then evaluate.

A: To reverse the order of integration in ∫04∫y2y2xy+1 dx dy and then to evaluate.

Q: Evaluate the integral. r1/v2 2 dx J1/2

A: Use formula of integration

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: Evaluate the integral. (Use C for the constant of integration.) dt t4 + 10

A:

Q: Evaluate the integral r4-x2 8x cos y dy dx r2 y – 4 by reversing the order of integration.

A: Evaluating the g8iven integral directly is not easy. So if we change the order of integration from…

Q: Evaluate V16-x² dx dx be? Explain Then, what would the value of the integral 1+V16-x 0.

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Q: Reverse the order of integration and then evaluate. a. S S, x² sin(xy)dxdy

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Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: Evaluate the integral.

A: ∫ex1+exdx Formula ∫xndx=xn+1n+1+C

Q: S S.(x + y)dxdy by reversing the order of integration.

A:

Q: S f(x.y)dxdy- Reverse the order of integration in 0,

A: The given integral is: To find the reverse order of integration.

Q: Evaluate the integral. (Use C for the constant of integration.) Vx dx

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Q: sketch, reverse and evaluate the integral dy dx

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Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: sin(e" – y) dy dx - In x

A: We have to find integral given in question.

Q: Evaluate the integral.

A:

Q: Reverse the order of integration in S(2xy + 1)dxdy and then evaluate.

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Q: Evaluate the integral. (Use C for the constant of integration.) t5 In(t) dt

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Q: a. Sx² e3*dx b. St sin t dt

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Q: Make a substitution to express the integrand as arational function and then evaluate the integral.

A: Given:           ∫e2xe2x+3ex+2dx

Q: 2- Evaluate and change the order of integration f(x + y) dxdy

A: We need to evaluate and change the order of the integration. first we graph the region bounded over…