Let 2 A := rx c5x+3y (4x + 8y + 82) dzdydx. Taking the internal integral we have 5x+3y (4x + 8y + 8z) dz = x+ xy+ Then r5æ+3y(4x + 8y+8z) dzdy O9 x° , and finally A =

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A: Given: ∫02∫02z∫y2ydxdydz

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A: Given ∫y-36y2+12y+6dy⇒6∫y-6y2+2y+1 dy⇒∫y-6y2+2y+1dy , write y as 16-1122-12y and…

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A: Partial fraction and indefinite Integration

Q: Let •3x+3y •2 A := (6x + 4y + 8z) dzdydx. Taking the internal integral we have 3x+3y (6x + 4y+ 8z)…

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A: The objective is to evaluate the integral ∫∫R3x-8y3x-ydA, where R is the parallelogram bounded by…

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Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a calculator we get:

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A: Solution:Given        y=x+2    2≤x≤7using ds=1+dydx2dxFormula:ddxxn=nxn-1

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A: a). We can write as: ∫∫D4yx3+2dA⇒∫02∫02x4yx3+2dydx   Now, I=∫02∫02x4yx3+2dydx...1   Solve,…

Q: Evaluate the given integral by making an appropriate change of variables. JJ₂ ³ 3 x - 8y dA, where R…

A: To Evaluate: The given integral by making an appropriate change of variables ∬R3x-8y3x-ydA, where R…

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Q: Fid

A: To find the triple integral ∫∫∫B24xy2z3dV , where B is the box B=0,a×0,b×0,c. dV=dzdydx.

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 3…

A: NOTE:- Due to the unavailability of a computer algebra system, the first question can't be solved as…

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A: Here, we need to evaluate, ∫ e5x+2dx. So,           ∫ e5x+2dxLet u=5x+2.=∫ eu15du=15·∫…

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Q: Evaluate the integral using the given substitution. u=8x + 10 /8x+10 A. +C 3/2 8(8x+10)* O B.…

A: Simply integrate

Q: b)compute the I = dz integral the c こ belo w (Zり2 1ver em (2) 2i Re (2) -2i

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Q: Suppose that f(x, y) 2a + 4y on the domain D = {(x, y) | 1 < I< 2, x² < y < 4}. Then the double…

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

Q: Calculate the double integral of f(x,y) over the triangle indicated in the following figure: y 3…

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Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

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Q: Use the Midpoint Rule with m = n = 2 to estimate the value of the integral IL x - 3y?) da where…

A: According to the given information, it is required to find the integral using mid point rule.

Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

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Q: Calculate the integral of f(x, y) = e*-2y over the parallelogram in Figure 7. y (6, 4) (1, 3) D (5,…

A: Let the given integral, f(x,y)=e3x−2y Now, from the figure of the parallelogram, let O(0,0), A(5,1),…

Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a computer algebra system we get

Q: Evaluate the given integral by making an appropriate change of variables. X – 7y dA, where R is the…

A: given Integral∬R3x-7y5x-ydA enclosed by lines  x-7y=0,   x-7y=9, 5x-y=2,   5x-y=7 Let x-7y=u and…

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Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Evaluate the triple integral: A 24 B 6 12 18 √₁³√₁² √²(x + y + (x+y+z)dydxdz

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Q: Verify Green's Theorem by evaluating both integrals aM | y? dx + x² dy = dA ax for the given path.…

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Q: 3. Set up the integral to find fffr x dV where T is the tetrahedron in the first octant under the…

A: To set up the integral to find ∭TxdV