Which of the following integral is the integral S, S S,(r² + y?)dzdydæ in the cylindrical coordinates? O a. * L L? r²dzdrdð O b. * r²dzdrd0 O c. * L S r³dzdrd0 C. O d. * RC r³dzdrd0 O e. S* So S5 r²0dzdrdð

Q: A) S16 S cos (16r x) dx dy. Osxs 2 Os ys x* B) Find the area between the parabolas x = y -1 and x =…

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Q: Is the following statement correct? The differential equation y' = (x² + y²)z has a unique solution…

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Q: oWhich of the following clifferential equation s is Separable? dy A. e B. dã C. d - Sin Cay) %3D D.…

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Q: 2文 A- dyda. adyda...

A: To evaluate the following integrals: A=∫02R∫0R2-x-R2dydx x=∫02R∫0R2-x-R2ydydx y=∫02R∫0R2-x-R2xdydx

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Q: 3. Evalnate. the. following.double.intagrals.by.comverting to Polar.Caa.r.dinates. 2 2 Anse. T(e-1)…

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Q: (2x + 3) csc²() dx + f 4 tan () dx = 2(2x + 3) cot (#) f(2x + 3) sec² () dx - 4 tan ) dx = 2(2x + 3)…

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A: Given integral is ∬Rx-2y3x-ydA where R is the parallelogram enclosed by x-2y=0, x-2y=4, 3x-y=1and…

Q: b-a Given the integral 2x dx, find the width xi = a + Ax·i and Ax = a. 1+ c. 2+ 2i b. 2+ 2 d. 4

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Q: dz The value of the integral Jc 22+9 where c is the circle z - 3i| = 4 is %3D

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Q: b. If x = t- 3, find L[(xe

A: Consider the given information. Lxe-x Put the value in the function. Lxe-x=Lt-3e-t+3=Lte-te3-3e-te3

Q: (5,1,2) Qnd Find the projection V of V to u Given V= (4,-3,1) is ON -bas in RB Determine the angle a…

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Q: What is the value of the closed integral cos(itz)/z with respect to z within the closed circle /z/ =…

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Q: 4. Express the following integral in spherical coordinates S² Sº √√4-2²-2² f(x, y, z) dx dz dy

A: The given problem is to express the given following integral in the spherical coordinates. We have…

Q: raluate [[- dxdydz the integral being extended to the positive octant of the V1-x-y-z? here x? +y…

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Q: dz wher the integral fe z2 +9 C = 4 is

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Q: Find the area of the part of the surface parametrized by F(u, v) = (v, 6 cos (2u), 6 sin(2u)), where…

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Q: (B) 62 (E) 62 QUESTION 13 13. Suppose we have a tank that is an inverted triangular prism as shown…

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Q: 4. Convert the integral from Cartesian coordinates to both cylindrical and spherical coordi- 1-T²…

A: The given problem is to convert the given triple integral in Cartesian coordinates to triple…

Q: Ex 15: Prove that : d du a) tanh u = sech² u dx dx

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Q: Rewrite using spherical coordinates the triple iterated integral and solve

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A: we will make chart as you mentioned in question for number to box.

Q: Find the length of L of the Curuc R Ct) = e2* cos (E) î +e?* sin (t) ĵ +ea* 1tsin (t) ĵ teat Ŕ over…

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Q: In this exercise you will prove Theorem 5.3. So consider triangle AABC. Let PE Int (ZABC) and Q &…

A: Given: consider triangle ABC , let P belongs to int(∠ABC) and Q belongs to int(∠ACB)

Q: In this exercise you will prove Theorem 5.3. So consider triangle AABC. Let PE Int (ZABC) and Q &…

A: Here we have given the triangle △ABC such that P∈Int∠ABC and Q∈Int∠ACB. We need to prove that…