If V is the volume of a cube with edge length and thecube expands as time passes, find dV/dt in terms of dx/dt .

Q: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

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Q: f Ine2x dx

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Q: O Calculate the integral y dydx

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

Q: Find the area of the surface that is obtained by rotating the curve Y = 0.25X? – 0.5 Log.X, 1<X< 2…

A: Given curve is, y=0.25x2-0.5logex  1≤x≤2 Let the area of the curve be S.

Q: evaluate using Integration by Parts.

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Q: Find the indefinte integral. (2x+ (2x+3)lnx dx'

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Q: Use the differential dV to estimate the change in volume of a sphere when the radius changes from 9…

A: ddxxn=n xn-1

Q: (c) 5tª Int dt

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Q: Sev dx (Hint: Integrate by parts with u-substitution)

A: To evaluate I=∫exdx

Q: Evaluate the following by changing the order of integration: dx dy. z/3

A: Explanation of the solution is given below....

Q: Show that the equalion Compatible 3olutions are and also find its रिकेपन nd देक.र

A: P2+q2 =1 given therefore 1x =pz P =x/z.  ...(1) q2 =1-p2      =(z2 -x2)/z2 q =z2-x2z ....(2)

Q: The area under the curve parametrized by x(t) = e", y(t) = 2et +1, where 0 St<1/3, is equal to.

A: As given, x(t) = e3t  y(t) = 2e3t + 1 where 0≤t≤13.

Q: Evaluate 6z dV where E is the region below 4x + y + 2z = 10 in the first octant. E

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Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

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

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Q: Find the integral ∫y (square root of y+2) dy

A: To find: ∫ yy+2dy

Q: (b) Compute the total area between the curve and the x-axis over the interval [-1,9]. y = f(t) 10…

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Q: Sketch the region of integration corresponding to y²e= drdy, (log æ)3 J = and evaluate J.

A: We will evaluate the given integral.

Q: ey dy ) dx.

A:

Q: The volume of a sphere is expanding wherer = 2t. What is the rate of change in volume with respect…

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

Q: ) Find the area of the surface that is obtained by rotating the curve Y = 0.25X² – 0.5 Log.X, 1<X<2…

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Q: =valuate the integral. (Rem. 25 + x2 dx

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Q: Find the Particuldr int egral Por the giren egh giren eqn dzy + 16y -4X + COS4X ニ

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Q: the inde Integrai. dx Vx -8

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Q: a

A: y = 3x Area = y*x A = 3x2 A(t) = 3x(t)2

Q: )Find the volume of the solid obtained by rotating the sine function between x 0 and x t about the…

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Q: 2 Evaluate the inteyral. dx dy dz taken. throughout the volumeofsphere 23=

A: We have to solve given integral:

Q: Determine whether the following statements is true or false, and explain why.

A: Answer: False.

Q: (a) If A  is the area of a circle with radius r  and the circle expands as time passes, find dA/dt…

A: Given: A is the area of a circle with radius r. To determine: dAdtin terms ofdrdt

Q: A certain close box having a square base has a volume of 100 in^3. Compute the rate of change of its…

A: Given is a box

Q: Write your own definite integral where the total area under the curve is 20.

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Q: 15. Use the table of integralsto evaleuate, the integral. ex dx

A: We have to evaluate the integral ∫ex1-e2x32dx by using the table of integrals.

Q: The volume of a right circular cylinder of radius X and height y is given by V= TXy, Suppose that…

A: Given Information : The volume of a right circular cylinder of radius x and height y is given by V =…

Q: O Reverre the order of integration and do not ewaluate dy dx Show the region.

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Q: dr Let A be the area of a circle with radius r. If dt = 4, find dA dt when r = 3.

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Q: Evaluate the integral. arctan(5t) dt

A: Here we evaluate the integral∫ arc tan 5t dt

Q: evaluate using Integration by Parts, substitution, or both if necessary.

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Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

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Q: 6. S ze 4z² dz

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Q: Supply the missing integrand and the limits of integration dx dy _dy ху

A: The given integral:∫-11∫1eydxdyxy

Q: h2 Evatuate the followingcartesian integrato by changing them inte equivalent Pelarintegrals: 3-…

A: Using Solution Subject Double integral by polar form

Q: find the integral of t sint cost dt

A: Integrand, I = t sint cost dtRecall the formula from trigonometry: sin2t = 2 sint costHence, sint…

Q: Let A be the area of a circle with radius rr. If dr/dt=5, find dA/dt when r=5.

A: See the details solution in below

Q: find Ihe area of ThI Surlace genecated by +Y about -akis; oEXEI

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Q: evaluate using Integration by Parts.

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Q: Evaluate the given double integral 1 dx dy

A: the given integral is  I= ∫-11∫-121dxdy

Q: V.r dx.

A: The given indefinite integral is: ∫xx-x23dx

Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Q: The value of the triple integral

A: Integration is the process of finding the anti-derivative function of the given function. The…