14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and the four vertical sides of the rectangle R, as in Figure 5.1.1. %3D

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

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Q: For question 3 – 4, use the Washer Method to determine the volume of the solid obtained by rotating…

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Q: 28 The region in the first quadrant bounded by y rotate about the line x = 4x2 , 3x + y = 7, and the…

A: It is given that, the first quadrant bounded by y=4x2,3x+y=7 and the y-axis is rotate about x=-4.…

Q: 1. Find the volume of the solid formed by revolving the region bounded by the graph of f (x) = -x² +…

A: Given problem:- Find the volume of the solid formed by revolving the region bounded by the graph of…

Q: SITUATION 03 Find the volume generated by the area bounded by the parabola x = Vay, and the line y b…

A:

Q: 2. Find the volume if the area bounded by the curve y = x³ +1, the x-axis and the limits of x=0 and…

A: Calculate the volume using washer method:  V=π∫03y2dx  =π∫03x3+12dx  =π∫03x6+3x3+1dx  =π377+3434+3…

Q: 15 - Which of the following is the volume of the object that occurs when the region bound by the y =…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the y…

Q: What is the area of the region bounded above by y = -3 MX. 54-3-2-1 1 2 3 4 45 O ভাল লাল নাল O O O…

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Q: 9. Find in two ways the area bounded by the parabola y = x², the y-axis, and the lines y = 1, y= 4.

A: Given,  The parabola y = x2  We have to find the area bounded by the parabola, y-axis and the lines…

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

A:

Q: 1. Find the area lying above the x-axis under the parabola y = 4x – x2.

A: The area lying above the x-axis under the parabola y=4x-x2

Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y

A:

Q: Find the volume of revolution about the x-axis for the given function and interval: f (x) = 3x − x2,…

A: The volume of revolution about x-axis for a function f(x) in the interval a, b is given by,…

Q: 1. Find the area bounded by the parabolas y= 4x and y'+12x = 36

A: Topic:- application of integration

Q: The volume of a solid is described by the double integral L 3 x’y dydx If the order of the integral…

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Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: 07) Compute the revol ving [- 8,8] volume of the solid obtained by the graph of the function fx)=…

A: we have given the function f(x)=7x5 on the interval [-8, 8]; We know the formula for the volume by…

Q: 2. The area bounded by y = -(x – 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about the…

A: Given: The area bounded by the curves which are: y=-12(x-1)2+4 and the lines x=1, y=2 and y=4 And…

Q: 1. Estimate the area under y = 2 In(5x) and above y = 2 for 4< x < 6.

A: we have to evaluate the area under the curve y=2ln(5x) and above y=2 for 4≤x≤6

Q: Example 28 Find the volume of the solid obtained when the region bounded by the curve y= 3x, x- axis…

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Q: .2 What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis…

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Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the volume generated if…

A: *to find:- generated volume about x-axis.

Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

A:

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 2. Find the volume of the solid whose base is the region bounded between the curve y=x² and the…

A:

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: 1. Find the area of the region bounded by the ves y = x³ – 5x + 6, y = 10 – 4x – 4x2 and the line x…

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Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the xy…

A: We sketch the region using a graphing calculator  The shaded region rotates around the y axis

Q: Suppose the following region is spinning rapidly around the x-axis. y = -1/² x + ²/ y 3 y=x 2 3 X -1…

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Q: Example 2.4.2. Find the volume of the solid of revolution of the region enclosed by the parabola y =…

A: Topic = Application of integration

Q: 1. Find the area bounded by y= (11 - x)1/2, the lines 3x = 2 and x = 10, and the X-axis. 2. Find…

A: The given problem is to find the area between given curves and also find the volume of solid…

Q: 3. a. Find the area of the region bounded by y= 2x2 + 10, y = 4x + 16, x = -4 and x = 5.

A: As per bartleby guidelines we only give first question answer.

Q: 1. Find the volume of the region between the graph of the function f(x, y) = 1 - (x² + y') and the…

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Q: Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross…

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Q: 1. Find the area bounded by the curve y = x^2, the x- axis, and the ordinates x = 1 and x = 3.

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Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: Below is the graph of y = x² 401 30 20- 10- -1 0 1 3 4 5 6 The area bounded by y = x² + 5 and the…

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Q: 6. Find the area bounded by: d. The curves y=x-4, y38-2x.

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Q: 8. Find the volume generated when the plane area bounded by y=-x²-3x + 6 and x + y - 3 = 0 is…

A: Finding the volume generated by revolving along x and y axis

Q: 2 3. Find the area of the unbounded region between the x-axis and y=- for x26. (x-4)

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Q: 1/6 Find the volume of the solid obtained by rotating the region bounded by and リー2) about the line…

A: Now , we will find the  volume of the solid  obtained by rotating the region bounded by the given…

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: R is the region bounded by y = -x² – 3x + 6 and x + y – 3 = 0 and it is revolved about x = -4.

A: Given that, R is the region bounded by y=-x2-3x+6 and x+y-3=0 and it is revolved about x=-4

Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 1- Calculate the area of the region which is bounded by: y = (x - 1)², y = (x-4)2, and y = 0.

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Q: - Find the total area between y = x/3- x and the x-axis for -1 sx< 8. %3D

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Q: 1. Find the area of the region bounded by y = x² - 3 and y = 5 - x².

A: This question can be solved using the concept of area bounded by two curves.