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

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Q: Calculate the iterated integral. 36 LTC + ar X dx

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Q: Use integration by parts to evaluate the indefinite integral. 3 arctan(5y) dy Answer = + C

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Q: Determine a definite integral that represents the arc length of r = 3e°, 0 < 0 <7. de 0.

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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…

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A: This question can be solved using the concept of differential equation.

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Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

Q: [? sinycos° ydy 2

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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: The total charge entering a terminal is given by q 5t sin 47 t mC. Calculate the cuIrent at t = 0.5…

A: The total charge q at a time t is given by the below equation. q=5tsin4πt mC To calculate the…

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. Given the integral dy dx, Sketch the region of integration, reverse the order of integration and…

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Q: 5. Set up the integral for the total work it takes to pump the water to 10 ft above the…

A: To set up the integral to calculate the total work to pump the water 10 ft above the given tank.

Q: Represent the length and area of each ellipse as definite integrals and use Simpson's rule with n =…

A: Given: r=11+0.9 cos(θ) Differentiate with respect to θ drdθ=0.9 sin(θ)(1+0.9 cos(θ))2 drdθ=0.9…

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

A: The edge length of the cube= x So the volume= V= x3

Q: The value of the double integral 45 dx dy is – 1890 1890 945 945 -

A: Given that ∫03∫0745dx     dy find out the value

Q: evaluate the triple intyyral dv where E is the solid 3. unded by Hhe Circular parab oloid

A: in cylindrical coordinate ,                     x2+y2=rz=zx=rcos(θ)y=rsin(θ)dv=rdzdrdθ the triple…

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: Determine a definite integral that represents the arc length of r = 5 cos(0), 0 <0<= do 0. 2/4

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Q: Evaluate the integral 2 // cos(x?) dx dy y by reversing the order of integration. With order…

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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: m, nEN imperding cosM X sin x tor Integral obtain re duction formula. u sing this Calalate integrol.…

A: Topic : integration

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: Each integral represents the volume of a solid.Describe the solid.

A: Given ∫0π22π cos2(x)dx

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A: ∫sinycosy2dy

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

A: Answer: False.

Q: Consider the following integral: siny dydx y By reversing the order of integration, the value of I…

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

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Q: The length x, width y and height z of a rectangular box are changing with time as x = 2+ sin 2t, y =…

A: length, x = 2 + sin2t width, y = 3 + cost height, z = 4 - sin3t   dVdt=? when t =π

Q: Set up an integral that represents the arc length of the function g(x)=sinxg(x)=sin⁡x for the…

A: We need to set up an integral that represents the arc length of the function g(x)=sinx for the…

Q: The area bounded by the ourves y= *", and y=2x iş revolved about the y-axis, Find the moment of…

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Q: A solid non-conducting sphere of radius 3 cm has a charge of +24 micro(u)C. A conducting spherical…

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Q: Evaluate the integral 2 sin(x dy by reversing the order of integration. With order reversed, sin(x…

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Q: Set up an integral that represents the arc length of the function g(x) = sin x for the interval [0,…

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Q: Determine a definite integral that represents the arc length of r = 6 cos(0), 0 <0< de 0. 下一2

A: Arc length

Q: Find the inde finite integral Slox+7)dx= =xP(L

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Q: Determine a definite integral that represents the arc length of r = 6e', 0 < 0 <9. %3D V3 6e20 +…

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 3  (  1/z)…

A: To integrate: ∫tan31zz2dz Let substitute t=1z Differentiating both sides, we get dtdz=-1z2-dt=1z2dz…

Q: Roro is looking at the iterated integral (x² + y²) dx dy and suggest to Mpho that the integral does…

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Q: b. Find by double integration the area enclosed by the curve r= a(1+ cos 0) between 0 = 0 and 0=T.…

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Q: A bar of material with a cross sectional area of ​​40 mm ? is subjected to tensile force of 120 N.…

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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

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Q: The value of the double integral || 10 dæ dy is - 80 O - 160 80 O 160

A: Given that ∫04∫0210dxdy find out the value of the double integral