State whether it would be quicker to evaluate this integral using horizontal lines (i.e. first along x, then y) or vertical lines (i.e. first along y, then x) and why.

Q: Evaluate the integral using appropriate substitution. an V3- a de + C

A: It is required to evaluate integral by substitution.

Q: Evaluate the integral LT :(+y°)etzc>xcy = ?

A: In this question, we have to evaluate the given triple integral. The iterated form of integral is…

Q: xp xy6x -x

A: The given integral ∫1x6x-x2dxThe integral formula,117. ∫duu2au-u2=-2au-u2au+C

Q: Express the integral in terms of the variable u, but do not evaluate it. In x -dx; u = Inx e3 rel4…

A:

Q: Evaluate the integral by integration by parts: TT √3 x² cos x dx

A: To evaluate the given integral by using integration by parts.∫0π2 x2 cos x dx

Q: Evaluate the double integral given by p2 sinOdrd0 TT JO

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Evaluate the integral by first modifying the form of the integr and then making an appropriate…

A: Integrating the function

Q: Evaluate the integral using integration by parts. |cot (8y)dy

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Q: Evaluate the iterated integral. LLL* dz

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Q: Evaluate the integrals

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Q: Express the integral in terms of the variable u, but do not evaluate it. In c dr; u = In x rels In c…

A: To determine: where  u = lnx

Q: Evaluate the integral. In(Vx) dx

A: Solution:

Q: Evaluate the iterated integral // VIte" dw dv.

A:

Q: Evaluate the integral. ∫t3  et dt

A: ∫t3  et dt  We need to evaluate the integral.

Q: Using only the definition of RS-integral, evaluate 2 ,2 d[x}.

A:

Q: What change of variables is suggested by an integral containing Vx? + 36?

A: For, an integral containing  x2+36 we can change variable by substituting, x=6tanθ, As it will get…

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: Integrate above questions.

Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: dr Evaluate the improper integral /, Tæ – 3)3/2 or state that it diverges.

A:

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: Here we have to integrate the given integral.

Q: Evaluate the integral by interpreting it in terms of area. 4 V16 – x dx

A:

Q: Evaluate the integral frever se 2. SS ー2 SinXy dsdx メ

A: Here we are given the following region of integration: The first part of region represent: x = y…

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integrals in ∫esec πt sec πt tan πt dt

A: Given: ∫esecπtsecπttanπtdt for evaluating this integral we substitute esecπt=u now differentiating…

Q: Express the integral in terms of the variable u, but do not evaluate it. In x dr; u = In r In r du

A: Given: I=∫e5e18lnxxdx   ...1

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Express the integral in terms of the variable u, but do not evaluat e21 In x dx; u = In x re21 In x…

A: We are asked to evaluate the integral.

Q: Evaluate the integral using integration by parts. 40 sec 20 do

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Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

A:

Q: Determine whether the integral is improper (x– 4) -'dx A Improper (B Not improper

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

A: Given: ∫72+x-4dx

Q: Identify the u, du, the form of the integral

A:

Q: the exaet V alde Of the integral. a

A: The objective is to show the exact value for the integral, ∫01axdx This can be re written as,…

Q: Express the integral in terms of the variable u, but do not evaluate it. ne25 In x dx; u = In x re25…

A:

Q: B. Re-write the triple integral *** following orders. 1. fff dydxdz 2. fff dxdydz dzdxdy as an…

A: Here firstly finding the curve using the limit then we saw that the region is the part of first…

Q: Evaluate the integral by making an appropriate change of variables. IL 5(x + y) e - da, where R is…

A:

Q: In da for the integral to be equal to What should a be in

A: This is calculus problem

Q: 14) ſe Vtanh® e" dy

A: Given that evaluate the integral

Q: Evaluate the integral using lIntegration by Partsisubstitution, or both if necessary. In(In 10x) dx…

A: Rewrite the given integral as shown below: ∫lnln10x10xdx=110·∫lnln10xxdx

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: Reverse the order of integratlon and then evaluate the Integral 10Tin6 Jinu! dx dy 9/10 et2

A:

Q: x In(2 + x³) dx

A:

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: Integrating the given function

Q: Express the integral in terms of the variable u, but do not evaluate it. re13 In x · d.x; u = In x e…

A:

Q: Evaluate the iterated integral. In6 In2 S." " exty dydx = Mi In6 In2 etty dydx

A: Topic = Integration

Q: b) Calculate the iterated integral by first reversing the order of integration. (1 ye? -dxdy

A: To calculate the iterated integral by first reversing the order of integration. ∫01∫y1ye2x3dxdy

Q: (b) Evaluate uV1 – uª du. by making a substitution and interpreting the resulting integral in terms…

A:

Q: Evaluate the integral by reversing the order of integration. So Soy e dædy =

A: Given: ∫01∫8y8ex2dxdy

Q: .Use integration by parts to evaluate the integral. In(z) dz = z2

A:

Q: Evaluate the integral by interpreting it in terms of areas.

A: