Find the volume of a sphere of radius r, centered at the origin, by slicing. Give an equation representing the volume of a slice, perpendicular to the x-axis, that you would use in a Riemann sum representing the volume of the region. Then write a definite integral representing the volume of the region and evaluate it exactly. Volume of slice The total volume over all slices is I d.x

Q: 4. Consider the region R in the first quadrant bounded by the graphs of y = x-1 and x = 5.

A: Given curve is                                          y=x-1, x=5 graph is

Q: Evaluate the given integral where C is the left half of the unit circle in ccd.

A: Note:- In given problem you mention "ccd" but one short form has different different full form. So,…

Q: Let the region R be the area enclosed by the function f (x) = e®, the horizontal line y = 4, and the…

A: Given that , fx=ex And  y=4. If the region R is the base of a solid such that each cross section…

Q: Use Calculus to find the volume of the following solid  The portion of a sphere with radius r and…

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Q: A volume is described as follows: 1. the base is the region bounded by y = - a² + 12x – 14 and y =…

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Q: The base of a three-dimensional figure is bound by the line y = x² on the interval [0, 2]. Vertical…

A: Formula: If the area of the cross-sections of a solid at x is Ax for a≤x≤b, then the volume of the…

Q: Let the region R be the area enclosed by the function f(x) = x³ + 1 and g(x) = x + 1.Find the volume…

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Q: Evaluate the volume: * The region is bounded by the curves x = y2 and x = 4 and is rotated about the…

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Q: A region in the first quadrant, bounded by y = x² +1 and y= 9– x² part A Compute the area. Compute…

A: Solution :-

Q: y=3+2x– x² and | about the y-axis.

A: Given:

Q: The base of a three-dimensional figure is bound by the y-axis and the curve x = + 2 on the interval…

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Q: Consider the volume of the region shown below, which shows a right circular cone with top radius 3…

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Q: ded region if it is revolved around the x-axis.

A: answer is in next step

Q: The region enclosed by the curve y = x ²- a ²and the x- axis is rotated by 90 deg about the x axis.…

A: The curve is :The x-axis is rotated by 90 degrees about the x-axis.The aim is to find an expression…

Q: x Let the region R be the area enclosed by the function f(x) = x² - 2, the horizontal line y = -3…

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Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R2 R2, first performs a…

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Q: Set up the volume when the region is revolved about the . x-axis (use vertical strips) - y-axis (use…

A: Assume that, we have given a region represented by y=fx or x=g-1y The volume when the region is…