Use differential to approximate the change in the volume of a sphere when its radius changes from 2 to 2.1. The volume of a sphere of radiusr is .3 4/3

Q: Use a graph to give a rough estimate of the area of theregion that lies beneath the given curve.…

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Q: The area enclosed by the curve y² = x(1-x) is given by .

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Q: Find the area enclosed by the x-axis  and the curve x = 1 + et y=  t - t 2

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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: Find the area between the curve x = 2r*, y = 31 +1 and the x-axis, 0<t<2 !!

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Q: The area bounded by the curve y=4- x2 · x-axis and the line is? 16 Ob. 11 Oc. 16 Od. 1 а. 5 3 3 3

A: The graph is shown below:

Q: Find the area between the curve of y = x + 2 and the x-axis on the inter 4 ਆਗੂਆਂ 2 4 -2- O O O 27 4…

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Q: 2. Find the area enclosed by the curve y2 = x6 (1- x²)³.

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Q: Find the area under the curve y = 5 over the interval [0, 1]. (4x + 4)2 Enter the exact answer. area…

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Q: 2. Find the area between the curve y = 3x2 + 2 and the line y = 2 * x- 3 from x = 0 to x = 3. Answer…

A: To find the area enclosed by the curves y=3x2+2 &amp; y=2x-3 from x=0 to x=3.

Q: Find the surface area generated by revolving about the y-axis the curves f(x) = 5x + 9 on [0, 7].…

A: We have to find the surface area of revolution.

Q: d) Find the volume of the solid formed when the area bounded by the curve y = 3x – x? and the lines…

A: The volume of the solid generated by the revolution of the area bounded by the curve y=f(x), x-axis…

Q: O Use differentials to approximate the increase in the area of a soap bubble when its volume…

A: Given query is to find approximate are increased.

Q: Find the area between the curve :       , and the positive semi-axis "X".

A: Given curve is y=e-xcos(x)

Q: Find the area under one arch of the cycloid x = a(t-sint) , y = a(1-cost)

A: Introduction: A cycloid is a two-dimensional curve that is constructed with half circles. One arc of…

Q: The area in the first quadrant under the curve y = e-x is revolved about the x-axis.  Find the…

A: Topic = Volume

Q: Show that if a solid figure is revolved about the x-axis, its volume of revolution is given by V= a…

A: To show that if a solid figure is revolved around the x-axis, its volume of revolution is given by…

Q: 1. Find the area bounded by the curves y?=2ax, y?=4ax-a? 2. By integration, show that the area of a…

A: To find the area of the region bounded by given curves.

Q: The area bounded by the curve y = vx, 2y + 3 = x and x-axis in the first quadrant is

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: Solution: The objective is to find the area of the surface

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: The given integral is, I=∫t3e-t2dt Take the value as u=t2dudt=2tdt=12tdu

Q: a

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

Q: 2.) Find the area between the curves y? = 2x and y 6-x

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Q: Use Simpson’s Rule with to estimate the arclength of the curve. Compare your answer with n=10  the…

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Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In x lying…

A: Solution We have to find the Surface area generated by revolving about the y-axis the part of curve…

Q: The volume V of a right circular cone of radius r and height h is given by V = ⅓ πr²h. Suppose that…

A: Solution:Given         V=13πr2hFormula:(uv)'=uv'+vu'To compare the change in volume of the cone with…

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: Find the area in the sec ond quadrant under 1 the curve x´y = e*. A =1 sq. units

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Q: Set up an integral for the length of one arch of the curve y = sin x, and by estimating the…

A: Given data: The given function is y=sinx. The expression for the length of the curve in one arch is,…

Q: Find the area between the curves. 4x y3e 8. x= 0, x= 3, y= 2 e y=e+ e

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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: Find the area between the curves. 3x x=0, x=3, y=2 e, y=e + e 3x The area between the curves is…

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

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Q: For the volume or a cylinder V = RR*H Find the total differential dV

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Q: O Use differentials to find a formula for the approximate volume of a thin cylindrical shell with…

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Q: Find the area under the curve: yA 4 y = 4 – x? 1 1

A: We find area by integration .

Q: Find the exact area between the curve f (x) = x³, the x-axis, and x=0 and x=4.

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Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: У— х — 2 y? = Find area using integration with respect to y-axis

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Q: B) By integration, determine the moment of inertia about the x-axis for the parabolic area shown in…

A: .

Q: Find the area under the curve y = -over the interval [0, 4]. (2x + 5)2 Enter the exact answer. area…

A: Find your answer below

Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is…

A: Given query is to find the rate of change of area.

Q: Find the area between the curve y = e X and the x-axis from x = 0 to o. square unit -2x 1

A: GIVEN DATA : Equation of the curve y=e-2x        TO FIND : Area under the curve and the x-axis from…

Q: 2. Find the area between the curves y = = ri and y = 2r1. %3D

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Q: Use the differential dV to estimate the change in volume of a sphere when the radius changes from 8…

A: We need to find dV. To find change in volume, we find derivative of given function and calculate it…

Q: Find the area between the curves y = e0.3se y = 1.9x + 1 from x = 0 to x and = 5. Area =

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Q: Write a differential formula that estimates the change in the volume V = of a sphere when the radius…

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