The graph above shows how the x-axis, the y-axis, the line y = -x + 3 and the curve %3D y = 2 sin x + 1create three bounded regions, labeled A, B, and C, in the first quadrant. Suppose region C is revolved about the x-axis. Which of the following integrals would describe the volume of the resulting solid? r2.850 Soso0 (-x+ 3)² – (2 sin x + 1)²dx r2.850 n J0,890 Sos90 (2 sin x + 1)² - (-†x+3)*dx O a fos00 (2 sin x + 1) – (-†x + 3)) *dx - 2.850 1)² - (-÷x + }'dx - 2.850 2

Q: 2. Sketch the region whose signed area is represented by the following definite integrals, and…

A: Definite integral is used to determine the area under the curve. It is denoted by the curve ∫abf(x)…

Q: The volume of the solid obtained by revolving the region between the curves y = x = 0 about the…

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Q: The shaded region shown in the figure above is trapped between the graphs of æ + y = 0 and ¤ = y² +…

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Q: For y = x3-7x2+15x-9 from x=1 and x=2 and above the x-axis, find the volume that results from…

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Q: 3. Find the volume generated if the function y =/1-x is revolved around the x-axis. (use the only…

A: If y=f(x) is a function, then the independent variable x is called the input of the function and the…

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Q: Which of the integrals represents the volume of the solid formed by revolving the shaded region…

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Q: Which of the integrals represents the volume of the solid formed by revolving the shaded region…

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Q: For each problem, find the volume of the solid that results when the region enclosed by the curves…

A: Solution is given below:

Q: The area bounded by y = x² and y = 2 – x² is revolved about the x-axis. Find the volume of the solid…

A: We have to find volume of solid revolution.

Q: Set up the definite integral required to find the area of the region between the graph of y = x² –…

A: Given: y=x2-20 & y=2x-5 Now find the point of intersection between the given curves;…

Q: Now we can say that the volume of the solid created by rotating the region under y = 8e-X and above…

A: We will find out all the unknown values.

Q: Set up the definite integral required to find the area of the region between the graph of y = a² –…

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Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/2), on the left by the…

A: Given that the function  y = 1x, x = 14 , y =1

Q: . Find a number k > 0 such that the area of the region bounded by the curves y = x², and y =k – x2…

A: As per as our guide line I am supposed to answer only one question from these 2 question Please…

Q: The area bounded by the parabolas y² = 4x and x² = 4y is revolved about the y-axis. Find the moment…

A: The given equation of the parabolas are, y2=4x and x2=4y.

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: Set up the definite integral required to find the area of the region between the graph of y = x2 –…

A: To set up the definite integral

Q: A solid is constructed between the graphs of y = f(x) and y = g(x) and the lines a = a and a = b so…

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Q: 5. Which of the following integrals would correctly compute the volume of the shape obtained by…

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Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given: y=6x, x=2 and x=4

Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Set up the definite integral required to find the area of the region between the graph of y = 15 –…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 13-²…

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Q: The base of a solid is the region in the first quadrant bounded by the line y = -1/2x + 2 and the…

A: At any point x calculate the area of cross section and integrate it over the interval.

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

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Q: The region bounded by y = 3x - 9 andy = -3x2 + 18 x - 9 revolved about the y-axis. Find the volume…

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Q: Set up the definite integral required to find the area of the region between the graph of y y = 6x +…

A: The area of the region between the graph of y=f(x) and y=g(x) is given by ∫abf(x)-g(x)dx, where a, b…

Q: find the volume (in units 3) generated when the region between the curves is rotated around the…

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Q: Set up the integral that gives the volume of the solid enclosed between the curves y=1/2x, x =2, x=4…

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Q: Step 2 So, the volume of the solid of revolution is Volume = V = Tt (25 – x)2 dx. To find the…

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Q: ( ) The region between the graphs of y = x2 and y = 2x is rotated around the line x = = 2. The…

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Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

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Q: Let M be the region in the first quadrant bounded above by the graph of y = 3x and below by the…

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Q: Find the total area of the region between the curve and the x-axis 1 xs3 4 ОА. 3 O A. OB. В. О С. 3…

A: *to find:- total area.

Q: Q6 If the region in the first quadrant that is bounded by y = sinx , y = cosx ,and the y- axis is…

A: Solution-

Q: THE REGION BOUNDED BY y = 205x - 1 AND THE X-AXIS IN THE INTERVAL πT 317 EX2 IS REVOLVED ABOUT 2 2…

A: The Shell formula for Revolution about a vertical line is used to evaluate the volume of the solid…

Q: Given is the area in the first quadrant bounded by x2 = 8y, the line x = 4 and the x-axis. What is…

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Q: Set up the definite integral required to find the area of the region between the graph of y = x2 –…

A: Given query is to find set-up the definite Integral to find the area between two graphs.

Q: Set up the definite integral required to find the area of the region between the graph of y = = x² y…

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Q: Consider the region R bounded by the line = 42- 8x and the parabola y = 27 – x². %3D To find the…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: THE AREA BETWEEN THE CURVES 2 4y = x² AND Y²³ = 4X 15 REVOLED ABOUT THE LINE X= -1. SOLVE FOR THE…

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Q: The region shown here is to be revolved about the x-axis to generate a solid. Which of the methods…

A: Given, the region revolved about the x-axis to generate solid.  Since there is some space between…

Q: Given the area of the region enclosed by y = 4 – x and y = -x+2, identify the integral that…

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Q: Given the area in the first quadrant bounded by x^2 = 8y, the line y - 2 = 0 and the y-axis. What is…

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Q: Write the integral needed to find the volume of the solid formed when the graph of the region…

A: Solve the following

Q: Set up the definite integral required to find the area of the region between the graph of y = x² –…

A: Area can be found as below :

Q: The area bounded by the curve y=cos2x and the x-axis is revolved about the x-axis. What is the…

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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.