Let R be the region bounded by the graphs of y = (x - 1)² – 1 and 3x = y? as shown below. Set up the (sum of) definite integral(s) equal to the following quantities. Do not simplify. %3D 1. Arc length of the portion of the graph of y = (x – 1)? – 1 which serves as a boundary of R 2. Area of R using vertical rectangles 3. Volume of the solid generated when R is revolved about the line x = washers method 4 using the (3, 3) R (0, 0) (1, –1) MNAS 2

Q: E. For the integral Ll- dy dr, do these three things, in order: y5 + 1 Graph (by hand) the region of…

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Q: Q2. Find the area enclosed by the curves y = sin x and y = cos x from x = 0 to x = n. sin)

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Q: (c) Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of…

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Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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Q: 1. Evaluate the integral . dA, where R is the region that lies between +y² the circles x + y? = a…

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Q: 1. In each part, use a definite integral to find the area of the region, and check your answer using…

A: 1. Area of the region is given by the definite integral ∫022−xdx∫022−xdx=2x−x2202…

Q: Set up the definite integral required to find the area of the region between the graph of y = 12 -…

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Q: rval [1,4] approxim

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Q: 5. Find the surface area of x = e³ that is of revolution about the y-axis on 0 ≤ y ≤ In 7.

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

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Q: Find the area of the region bounded below by the curve y , to the left by the curve y = || cos(x)…

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Q: valuate, numerically, the following integrals: b) Sor sinx dx by using Simpson's rule ( take n = 4 )

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Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 – x…

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Q: Use the graph shown below to estimate I f(x) dx. 8. f(x)- 6. 4 1 4 This integral represents the area…

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Q: Draw the region whose area is given by the definite integral x² dx a) b)

A: a) Here, the plot contain the curve y=x2 bounded by lines x=2 and x=4.

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Q: The area of the surface obtained by revolving the curve x= Vy+4 for a-4.)

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Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = T, using 4 trapezoids.…

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Q: Split the region between the two curves into two smaller regions, then determine the area (in units)…

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Q: D. Set-up the definite integral that will give the area of the surface generated by revolving the…

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Q: Find the area on the graph? Integral-related question

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Q: 1. Approximate the area under the curve of y = e¯** from x = 0 to x = 1 using: a. R4 h Le %3D

A: Reimann sum