1. Show by integration that the volume V of a right circular cylinder with base radius r and height h is V = nr’h

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

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: Evaluate the iterated integral " SL* x² sin y dy dz dx .

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Q: Evaluate the tollowing Integral csc “(+w)cot" (+w)d 4

A: Problem is related to integral of the function based on the trigonometric concept. General formula…

Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: # 1) If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt…

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Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Find the exact value of the integral using formulas from geometry. 5 (3+ 2x)dx 1

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Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Please check the region, given region is not bounded, we consider the region bounded by curve, x=0,…

Q: 14 Find the integrals using integration by parts. b. JF In /rdx In a. fx(x + 4)°dx c. fr'e"dx d.…

A: Just multiply by 1and go ahead.

Q: What is the integrating factor of (1 + cos z) y' = sin z (sin z + sin rcoSI y) - CSC I sin z O1 +…

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Q: Find ke ende finite integral. cuse c for Ge Constant of entyration) J Sin 39 Jcos 34 de (the + are…

A: We need to solve integral.

Q: Question 3 Selve the linear Ruation: dy 3. Integral faualian.

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Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

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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: 2. Evaluate the double integral: Lo Sch sin (2³) VVT (Hint: Change the order of integration to dy…

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Q: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

Q: 2. Evaluade integral.. iterated double ze^ dx dy

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Q: Evaluate the iterated integral. (3x + 4y3) dx dy

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Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

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: To evaluate the integral |x sin xcos x dx using integration by parts, the convenient choice is, H=…

A: a. Given integral is ∫ xtan2xdx. Considering u=x and v'=tan2x is the convenient choice for…

Q: Evaluate the iterated integral.

A: The given integral is ∫01∫0y6x+5y3dxdy

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

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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: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

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: The value of integral .dz is (z – 1)?

A:

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: Differential

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: Calculate the iterated integral.

A: To calculate the iterated integral ∫05∫142xy4+3dydx

Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: Can you help me step by step?

A: dA/dt may be written as,

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: Evaluate the iterated integral. (2х — 4у) dy dx Exact number, no tolerance. (2x – 4y) dy dx = i -1

A: The given integral is: I=∫111∫-11(2x-4y) dy dx

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

A: The given integral:∫-11∫1eydxdyxy

Q: 9 Set up an integral for the length of the Curve, yこx,05x<ト

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Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: @ Eualuate the integral dx dy dz taken throughout the volume of

A: Concept:

Q: Evaluate the integrals ∫tan (ln y)/y dy

A: Given ∫tan(ln(y))ydy

Q: evaluate using Integration by Parts.

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…