Which of the following is incorrect about the propertics of an integral? s F(x)dx = - f(x)dx Sa kf(x)dx = k ff(x)dx Option 1 O Option 2 sN)dx = 0

Q: 4. Rewrite the following integral in the order dy dz dx 1-7 f(x, y, z) dx dy dz

A: In this question we have to rewrite the given integral in order of dy dz dx.

Q: Which among the following is an improper integral? In3 ex In2 4- ex 1 dx X/16 - Inx 1 dx x Inx In2 1…

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Q: Evaluate the integral. 16 In(y) dy Vy

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

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: If | f(z)dx f(x)dx + what are the bounds of integration for the first integral? a = and b =

A: Given that ∫abfxdx=∫−47fxdx+∫78fxdx−∫−41fxdx

Q: If {(-)dn = [ f(=)dz + [ 1 f(x)dz what are the bounds of integration for the first integral? a = and…

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Q: dx Evaluate the improper integral x(In x)?

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Q: Evaluate the integral using integration by parts. e4 x* In (x)dx 1

A: To Evaluate:

Q: The integral TT tan x sec?x dx 2 O none of them is an impróper integral of type I that diverges is…

A: Improper integral

Q: Evaluate the itorated integral. 24 ,xty *ty dx dy

A: First we need to calculate integral with respect to x then y

Q: Evaluate the following integral. In 3 Vz In (öy) ex+y? -z dx dy dz 1 1 In (5y) In 3 Vz In (öy) ex+y…

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Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

Q: Get the integral of ſe*sin x dx using integration by parts c. e*(sinx – cos x) + c D. -e*(sinx – cos…

A: The integration of the integral is exsinx.

Q: Evaluate the iterated integral. (x + 5)dy dx 8 (x + 5)dy dx = i

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Q: Which of the following integrals, if either, calculates the area of the shaded region shown here?…

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Q: Evaluate the iterated integral. (x + 2)dy dx 6. (x+2)dy dx = i

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Q: B. Set up the integral for the area enclosed by y = 5x – x² and y = x from x =-2 to 6. Do not solve.

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Q: Evaluate the iterated integral. In 4 In3 2x+Y dy dx 0 1 **y In 4 In 3 e2x + Y dy dx = 0 1 (Type an…

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Q: Which ONE of the following is a PROPER integral? OA. dx In-x OB. dx X+ sin2r OC. 2x dx 7x2- 3x OD.…

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Q: Determine the exact value of the multiple integral -In 101 ex-y+z dx dy dz – In z JIn 99

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Q: Assuming that f(x, y) is an integrable function, which of the two cross-sections would you choose to…

A: As per the question we are given a 2d region of integration defined as the area bounded by : y = ex…

Q: Evaluate the integral. In(x) dx, y > 0

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Q: Evaluate the integral. y In(x) dx, y > 0

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

A: Given: The improper integrals f(x)dx from limit -infinity to zero.

Q: Which of the following is the general power formula for integrals whenever n # -1? Sx"dx = x"+1 + C…

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

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

Q: Use the Comparison Theorem to determine which of the following integrals converge. (1) { arctan x dx…

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Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: Which of the following is incorrect about the properties of an integral? rx)dx = - L, f(x)dx Si…

A: As we know that from property of definite integration.

Q: Extend your knowledge of double integrals to evaluate the triple integral So So S**** f(x, y, z) dz…

A: Given that I=∫01∫0x∫01+x+yf(x,y,z) dzdydxTo extend the double integral to triple integral.

Q: Which of the following integrals are improper? Why?  integral -1 to 1    ( 1/ x 2 -x -2 ) dx

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Q: Which one of the iterated integrals below are equivalent to (There is a penalty for incorrect…

A: To find- Which one of the iterated integrals below are equivalent to ∫-11dy ∫y21dx ∫01-xdz? ∫01dz…

Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: Evaluate the integral [(x+2y)dy.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral. (x + 4y) dy

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Q: Evaluate the improper integrals: (a): xe ,-x dx •4 dx (b) V4-x

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

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Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: 2. Evaluate the integral by interpreting it in terms of areas: J | sin x dx. -T

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Q: 1. Evaluate the integral using Integration by Parts. (a). S In(Inx) dx.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate the iterates integral: S, (x- y) dy dx

A: By integration property

Q: 4. S x² e*dx

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Q: Which among the following is an improper integral? 1 A x[In?(3x) – 4] Inx x[In*x- 1] ` .0.5 1 dx…

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

A: Given integral is,

Q: Which of the following integrals represents the surafce area of the curve y = 3x +1 for 2 <x<5? S=…

A: Directly use the formula for the surface area of the curve and substitute the given equation of the…

Q: Evaluate the integral In 23 In y s s ex+y dx dy.

A: Given: ∫1ln23∫0lnyex+ydxdy

Q: Evaluate the improper integral if it exists dxp: 2.10 0.20 The improper integral diverges 30 2/2 40

A: Option (3) is correct. Integral diverges.

Q: If f(z)dz = f(x)dæ + f(x)dx 7 what are the bounds of integration for the first integral? a = and b =

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