8. Integrate by parts: a) St csc? t dt b) S x2 In x dx

Q: Evaluate the iterated integral. * Tt/2 [y/8 7/y sin y dz dx dy Jo Jo

A: Given,  ∫0π/2∫0y/8∫07/ysin y dz dx dy

Q: Evaluate the following triple integral over half unit ball below y-plane(B), //| Væ² + y? + 2² dV. B

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Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

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Q: Evaluate the triple integral. 3x dV, where E = {(x, y, z) I 0 s y s 2, 0sxs V4- y², 0 s z s 2y}

A: Given region is E=x,y,z/0≤y≤2,0≤x≤4−y2,0≤z≤2y We have to evaluate the triple integral ∭E3xdV in…

Q: If y(w)dw 11 3 and y(w)dw = 6.7 what does the following integral equal? y(w)dw = %3D 3

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Q: Evaluate the double integral. |/ (2x + y) dA, D = {(x, y) | 1 < y< 4, y – 3 < x :

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Q: Evaluate the double integral. // (2x + y) da, D = {(x, y) | 1 s y s 4, y – 3 sxs 3}

A: Evaluate the integral

Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² +…

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Q: Evaluate the iterated integral. ITT 4ze dy dx dz

A: ∫14∫01∫0x34ze-x4dydxdz

Q: Evaluate the triple integral. y dV, where E = {(x, y, z) | 0 < x< 8,0 s y s x, x – yszsx + y}

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Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Evaluate the iterated integral. yz dx dz dy 45 в) 34 47/3 D) 5

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Q: Consider the triple integral I = S S“(y² – 6z)dydzdx. -

A: ∫02∫x21∫0xzy2-6zdydzdx=∫02∫x21z3x33-6z2xdzdx=∫02x31-x812-6x13-x63dx=31.88888…

Q: Evaluate the iterated integral: S", Si yz dx dz dy.

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Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact,…

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Q: The value of the integral dz , over the Contour C |2 – 2| = 2 is equal 2Ti 2rie 2rie

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

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Q: aluate the iterated integral. || 5x²sin(y) dy dz dx =

A: Given: ∫0π∫05x∫0xz5x2sinydydzdx

Q: Use SphericalL coerdinates to evaluate the +र |राज्ट | . triple integral SSS x°*y@;=? d V, Where E…

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Q: ) USE THE METHOD OF VARIATON OF PARAMCTERS TO SULVE THE GIVEN ODE 8" +y'= secx Sec'x %3D

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Q: Evaluate the iterated integral.

A: Consider the following integral: ∫13∫0y4x2+y2dxdy=I Consider the following formula:…

Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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Q: Evaluate the iterated integral. x2 3ze dy dx dz Jo

A: triple integration

Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: (c) Estimate the following double integral: (x + y + 10) dz dy, D where D = {(x, y) | a² +y? < 4}.

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Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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Q: a dV E where E is bounded by the cylinder a? + y? = 9, 0 0.

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Q: 5. * m/2 X sen y dy dx n/2 6. Ja/6 EL cos y dy dx

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Q: Evaluate the triple integral. y dV, where E {(x, y, z) | 0 < x < 2, 0 < y < x, x – y < z < x + y}

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Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Sl, Cos () dxdy sin (1) Prove that: I = JJ. x+y where R the region bounded by x+ y = 1,x = 0,y = 0

A: Here we have to prove that       ∫∫R Cos{(x-y)/(x+y)}dxdy = sin(1)/2  Where R is the region bounded…

Q: Calculate the line integral a) |y ds, C:x =ť², y = 2t, 0 <t < 3 C

A: Use parametric to solve

Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: SI 1 Evaluate the triple integral S dx dy dz xyz 1

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Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: Vx 3+4x+8 dx 2 vã (Vx?)

A: The given function is x34+4x+8xx23 We have to identify u and du and the form of the integral of this…

Q: (a) SII+y+z) dz dy dx

A: The given triple integral is: I=∫01∫01∫01 x2+y2+z2 dz dy dx

Q: Evaluate the triple integral. SI. {(x, v, z) | 0 < y s 2, 0 < x < V4 - y?, 0 < z < 5y} 2x dV, where…

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Q: Evaluate the iterated integral. 5x 15x? sin y dy dz dx Jo

A: Given ∫0π∫05x∫0xz15x2sinydydzdx Evaluate the iterated integral

Q: Calculate the double integral. 2x dA, R = [0, 2] × [0, 1] 1 + xy %3D IR

A: to calculate ∫∫R2x1+xydA; R=0,2×0,1

Q: Evaluate the iterated integral. SIT stad dy dx dz 5ze

A: Answer and explanation is given below...

Q: Evaluate the triple iterated integral. 2 4 xyz' dx dy dz Jo Jo J -1

A: Here we have to solve the givne triple integral I=∫02∫01∫-14xyz3dxdydz

Q: tes to evaluate the triple integral e Vz² + y² + pounded by the spheres z² + y² + z² = 4 and z? + y…

A: Given, ∫∫∫Ee-x2+y2+z2x2+y2+z2dV E is the region bounded by spheres x2+y2+z2=4 and x2+y2+z2=25.

Q: y³ Vy² + 4 dy Let u = y? 2

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Q: 7te', Int )dt Edit i+ Edit j+C

A: