2. A tank in the shape of a cone (as shown below) is filled with water. Assuming the density of water is 1000 kg/m³and the constant for gravity is 9.8 m/s², find an integral that represents the work needed to empty the tank through a pipe 4 meters above the tank. 12m | 36m

Q: 0. Everlueik he integral (ez)Esmz dz, where Ci12|=1, by any and two methods Compare the geselts.

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Q: Which of the following integrals represents the length of the curve y = 2*, 0 < x < 3? 3 VI+ 2* dx…

A: Given function :

Q: 1 Inr dr. + evaluate the improper integral

A:

Q: 3. a. Use a computer algebra system to evaluate the following integrals. i. : / Inz dz i. / 2 ln z…

A: The solution are next step

Q: where d! x*ry*< a² 2.

A: Change in polor coordinate.

Q: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

A:

Q: Evaluate the iterated integral. In 4 In 3 e 2x+Y dy dx 0 1 In 4 In 3 | | e 2x+ydy | dx = 0 1 (Type…

A: Solve the following integral

Q: area ZA (xy) dx dy y/3 10.

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Q: Evaluate the integral by integrating with respect to​ x, y, and z.

A: Given integral is,

Q: dy dr x+ y 33. a dz dy x² + y 34.

A: .

Q: Use a change of variables to evaluate the defınite integral. 5 So de V1+z

A: We have to find

Q: Find the work integral of F = ⟨y^2, x⟩ along the line segment C starting from P(0, 1) and ending at…

A:

Q: Evaluate the integral. integral from 1 to 3 and integral from 0 to lnx  e^y dydx

A:

Q: To find the arclength of y = 4x2 + 1 from x = 0 to x = 5, which is the correct integral? 5 OL = V1 +…

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

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Q: lEvaluate the integral ×+ス de . x²+2x linlx?Cx+z)e X+2 (x+2)²|&7C Dinlx (x+2)I +c E) Inl x て) 12

A: Topic = Integration

Q: Reverse the order of integration in the iterated integral and then evaluate the integral. NE p2-x*…

A: The region of integration is

Q: 4. Calculate the following iterated integrals by hand. Show all steps. (a) (b) (c) -dr dy

A:

Q: valuate * f(t) e- st dt if f(t) =t². Show your proper solution in evaluating improper integrals.…

A:

Q: E valuate the improper integral Sma Xe* de Ina

A:

Q: Determine the value of the following integral using the remainder method 24πί2?dz I = l-10 (z – 1)(z…

A: The given problem is to evaluate the integral using the remainder method, we have to find the poles…

Q: A tank is full of water. 1m 6m 12m 3 Set up an integral to find the work required to pump the water…

A: Given the figure with the data,  We will take a slice at a height y from the ground. Let r be the…

Q: Rewrite the iterated integrals in the order dzdydx 11-y? 1-y SS S f(x, y, z)dædzdy 00

A: The given integral is: ∫01∫01-y2∫01-y f(x, y, z) dx dz dy

Q: To find the arclength of y = 2x – 3 from = 0 to x = 4, which is the correct integral? OL = V1+ 4x²dx…

A: I have appended the formula used in the solution part.

Q: Evaluate the iterated integral. •x5 V 64 – x6 dy dx /o Jo

A: The given integral is:∫02∫0x564-x6dydxWe need to evaluate the integral.

Q: 7. Extend your knowledge of double integrals to evaluate the triple integral Si Si S (x,y.z) dz dy…

A: Find: the value of ∫01∫0x∫01+x+y fx, y, z  dz dy dx.

Q: B D cF I| f(x, y, z) dV = dz d

A: We have to evaluate the integral:

Q: a) Evaluate the Integrals: 2x2 + 3 x(x + 1)2 b) Find a horizontal line y = k that divides the area…

A: (a) part Consider the given integral ∫2x2+3xx+12dx Now,…

Q: Set up the definite integral required to find the area of the region between the graph of y = 12 –…

A:

Q: Suppose that you push a book across a 6-meter-long tableby exerting a force f(x) at each point from…

A: You push a book across a 6-meter-long table by exerting a force fx at each point from x=0 to  x=6.

Q: b) Determine the volume of D = 5[ 1 dV using integral -zx.

A: The volume of a solid V is given by V=∬∫v 1 dvwhere limits of x,y and z can be found from the given…

Q: (c) How large do we have to choose n so that the approximations Tn and M, to the integral in part…

A: Solution c: We have integration is ∫1231e1xdx, here a=1, b=2 So, let f(x)=31e1x So f''(x)=-31e1xx2…

Q: (8) Evaluate the contour integral: 2021 e1/z² dz. Izl=2

A:

Q: ^ du 1 1+2 Sinn

A: Solving the given integral using the substitution method Also using the formula for the integration…

Q: A 30 chain weighing 10 lb/ft that is coiled on the ground. Which of the following represents the…

A: We are gonna lift the chain 0 to 30 Work = 10(30 - y)  So option A is correct.

Q: Which of the tollowing integrals gives the ength of the graph y=18 between X= a and a. a 1X2+X dx b.…

A: We have to find the length of the graph  y=x  between x=a and x=b where  0&lt;a&lt;b.

Q: 4. Compute cach of the following iterated integrals by reversing the order of integration. sin (r)…

A:

Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: Given integral ∫12∫02x-x21x2+y22dydx. The objective is to evaluate the integral. First we change x…

Q: If h(z)dz = 16 and 7 | h(z)dz = 7.1 what does the following integral equal? |h(2)dz=|

A: ∫-37 h(z) dz =16   and ∫07 h(z) dz =7.1

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 1 the polor integral…

A:

Q: • 2π 0 rieit 20 + reit dt

A: The given integral is                               ∫02πrieitz0+reitdt

Q: If k € R+, which of the following expressions or triple integrals is NOT equal to the volume of a…

A: Option b is not true

Q: Q.3 Find the double integral for SI, x? dydx, where R between y = 1/x,y x and x = 2

A:

Q: Use Trapezoidal method to find the following integral given h = 0.2. * 1 S In(x + 1)dx 0.3846 O…

A:

Q: F-(2x-3)も- 2xyj-42kノexauate SSS v.P dv, x 0,yo, 2, 2×4 2ytz=4

A:

Q: 1. Use Numerical methods to approximate the following integrals (a) (x +y)dxdy , n = m = 3

A: Trapezoidal rule: ∫cd∫abf(x, y)dxdy=h2fa, y+2fa+h, y+fa+2h, y+⋯+fa+n-1h, y+fb, ydy, where h=b-an.…

Q: Evaluate the integrals .SiPi+7 j+(t+1)k] 4 S (sinti+(1+cost)j] -a4

A: In the given question, we have to find the integral of  ∫01[t3i+7j+(t+1)k] ∫-π4π4[sinti+(1+cost)j]

Q: Evaluate the integral. H (z(1 – 2z)*) dz =

A: topic - definite integral

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ y + 3/2y3 - 8y dy

A:

Q: 2- Assume that x, y e R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: Consider the given figure in the question. We have to evaluate I=∫x=0∞1x3+1dx in the given contour…