Write a definite integral which computes the area of a surface of revolution 3 1 from rotating y=-x² 3 on [0,8] around the x-axis. Do not integrate it, just write it.

Q: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8<x<π/8

Q: Write an integral for the area of the surface generated by revolving the curve y = cos(4x) about the…

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Q: Use a double integral to find the area of the shaded region.

A: The formula for the area of a region of a polar curve, r(θ) bounded by θ=a to θ=b in the polar…

Q: Write the integral that gives the area of the surface generated when the curve y = 1 + sin æ on the…

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Q: Use a double integral to find the area of the region that lies outside of r=2 and inside of…

A: This question is from double integral.

Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A: Integration by parts:∫uvdx = 4∫vdx - ∫[ddx(u)∫ vdx]dx

Q: Set up and evaluate the definite integral for the area of the surface x2 y = 1 - 16 OsxS 4 2n dx =

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Q: Find the complete integral xp+3yq D2 (z - xq). 2 2 the

A: Consider the given equation: The objective is to find the complete integral of given equation.

Q: Evaluate the integral || (x + y)e**-y dA by making an appropriate change of

A: Given data:     The given integral is: . The first equation is: x-y=0 The second equation is x-y=3.…

Q: In ly-y-cf dy

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Q: Evaluate the iterated integral by converting to lar coordinates. /1-(х-1)2 x² + y² dy dx

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Q: Evaluate the inner integral by Simpson's rule with n = 5 and outer integral by rectangular rule with…

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Q: 7) (g) Set up and evaluate the definite integral for the area of the surface generated by revolving…

A: we use integration formula for area of surface rotating about x-axis..

Q: Set up the integral to find the length of J (X) = e from x = You don't have to integrate it. 0 to x…

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Q: Evaluate the integration: r sin(20)drd0 Over the area in the first quadrant bounded between two…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(æ) dz…

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Q: Write a definite integral that represents the area of the shaded region and compute the integral…

A: We have the given curve as y=-x+4 At y=0, we get the value of x as 0=-x+4x=4

Q: use a double integral to find the area of the shaded region.

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Q: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: fx=x3 is a polynomial function. It is continuous in the interval 0,3.

Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: 20. V9 – x² dx

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Q: Use the Trapezoidal Rule to approximate the integral of e^(3/x) dx from 2 to 3 with n=4 . Round the…

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

A: The solution are next step

Q: Use a double integral to find the area bounded by y = x², y = -x+ 12, and y = 4x + 12.

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Q: Use the Trapezoidal Rule to approximate the given integral with n= 6. Show your work 1 dx

A: Topic- Integration

Q: Express the iterated integral fo SY² d as a non-iterated (i.e. single) integral in Y/1-y² terms of…

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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: sin Bt dt

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Q: Set up a definite integral to find the length of the curve  y= (3/4)x(4/3) - (3/8)x(2/3) over the…

A: The given curve is,

Q: Consider the following curve. y = x³, osxS 5 Set up an integral in terms of x that can be used to…

A: The surface area of revolution about the x-axis is: S=2π∫abf(x)1+f'(x)2dx If the function is,…

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: To evaluate the integral: ∫022x-x3dx Evaluating the integral.…

Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: 4. Let f(x) = x^3 over the interval [0, 1]. Find the surface area of the surface generatedby…

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Q: 3(sin y- cos y)* dy cos y

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

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Q: Use a double integral to find the EXACT area enclosed by the graph of r = 3+3 cos 0. 8=1/2

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Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: we have to evaluate the integral: ∫01x3-3x2dx using the definition of integral, ∫abf(x)dx=limn→∞∆x…

Q: Write the integral used to evaluate the surface area when the given curve is rotated about the…

A: The objective is to write the integral used to evaluate the surface area when the curve is rotated…

Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Use double integral to find the average temperature of 1 (x, y) = tion of o ploto 0<rs4 and 0< y3 5…

A: Given,      T(x, y)=12-6x2-4y2,       0≤x≤4 and 0≤y≤5

Q: Evaluate the integral -5earctan(y) - dy 1+ y?

A: We have to evaluate the integral.

Q: - SxS Write an integral for the area of the surface generated by revolving the curve y = cos (3x)…

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Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: Consider the given integral as  2π∫-5581-x2dx

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.