Example 4 Use double integration to calculate the area of the region 2 encolsed by y =x and x +y = 2.

Q: Find the area bounded by the graphs of y = 4- x^2 and y = x - 5 between x= 0 and x= 2. Sketch the…

A: Given query is to find the the area of region bounded by the curves.

Q: sketch the described regions of integration. 0 ≤ x ≤ 3, 0 ≤ y ≤ 2x

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Q: Example 5 Find the area of the region enclosed by x = y² and y = x – 2, integrating with respect to…

A: We have to solve given problem:

Q: sketch the described regions of integration. 0≤y ≤ 8, 1/4 y≤ x ≤ y1/3

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 4x, y = 0

A: We first find where the two equations meet.  We plug y=0 in the first equation and find x

Q: sketch the described regions of integration.0 ≤ y ≤ 1, 0 ≤ x ≤ sin-1 y

A: Given: 0≤y≤1 0≤x≤sin-1y

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

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Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

A: Given equation y=-x2+6x,  y=0. The objective is to find the area of the region. "Since you have…

Q: Find the area of the region bounded by the graphs of the equations. x = 1, x = e, y = 0 y

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Q: Sketch the region of integration. (Select the correct graph.) "In 3 dy dx In y y y

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Q: OFind the area of the region bounded by y = e* , y = e* andx=1.

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Q: The region bounded by y = 3x – x² and y = -x %3D

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Q: Find the area bounded by y = 2; y = √x + 2; and y = 2 - x. Show your solution below.

A: We are given :  y=2  y=x+2 y=2-x First of all we will plot the graph for these 3 curves.

Q: Find the area of the region bounded by x = y^2 - 2, y = ln x, y = -1, and y = 1. Sketch the region.

A: We graph the functions first. We need to find the area of the shaded region.y=lnx => x= e^y

Q: 8. Sketch the region of integration and then give an equivalent double integral with the order of…

A: To draw the region of integration

Q: Find the area of the region bounded by the graphs of the equations.                  y = √x(1 − x),…

A: Given function is y=x1-x. Graph the function as shown below.

Q: Region bounded by y = 1 − x2 and y = 0

A: To graph the region bounded by, y = 1 − x2 and y = 0

Q: Sketch the graph of the curve y z (x-6)(x-7)(x-8) Shade the area of the region bounded by the curve,…

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Q: Sketch the region of integration. (Select the correct graph.) in 5 6 3 1 2 3 6 2 1 2 3 4 Evaluate…

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Q: Find the area of the region bounded by the graphs of the equations               y = cos2 x, y =…

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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: Find the area of the region bounded by the graphs of the equations. x-1 y = √x-1, y 2

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Q: Find the area of the region bounded by the 3 graphs of the equations y = sin x, y = sin° x, 0, and x…

A: Consider the given curves. Equate (1) and (2) and calculate the x where (1) and (2) are equal.

Q: How are substitutions in triple integrals pictured as transformations of three-dimensional regions?…

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Q: Sketch the graph of the curve y (x-p)(x-p-1)(x-p- 2) Shade the area of the region bounded by the…

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Q: Sketch the graph of the curve y = (x – p)(x – p – 1)(x - p – 2) Shade the area of the region bounded…

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Q: Question 3 of 8 1 Evaluate the double integral by reversing the order of integration y sin(æy?) dydz…

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Q: y =-z +4x, y= 0

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 8x, y = 0

A: Let us plot the region.

Q: sketch the region of integration ireverse and eva luate az ex J S dy dx

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Q: 2. Express the shaded area of the region shown below by double integrals of order of integration (1)…

A: find area using double integration

Q: Problem - 6: Evaluate the integral using 4 3 integration by parts technique : | x Vx+4 dx

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Q: Example 1: Determine the volume of the solid obtained by rotating the region bounded by f(x)=x² –…

A: Given function   Graph the given function using graphing calculator . Also graph x=1 and x=4…

Q: Sketch the graph of the curve y (x-p)(x-p-1)(x-p-2) Shade the area of the region bounded by the…

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Q: > Example 5 with respect to y. Find the area of the region enclosed by x= y and y= x – 2.…

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Q: Use double integration to calculate the area of the region 2 encolsed ye and x+y=2.

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Q: sketch region 4 reverse Integration then evalute (4 x +2) dy dX x 2

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Q: find the area of the region bounded by y = x+2 and y=x^2.Use double integral to solve the question.

A: Solution-

Q: Sketch the region corresponding to the double integral 1+√3 1-y² √ dx dy and reverse the order of…

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Q: Sketch the region enclose by y=x2-9x+21 and y = -x2+11x-27. Decide whether to integrate with respect…

A: Given data is : y=x2-9x+21 and y=-x2+11x-27  To sketch the region.

Q: Sketch the graph of the curve y = (x- p(x -p- 1)(x -p- 2) Shade the area of the region bounded by…

A: The given curve is as follows - y = (x-p)(x-p-1)(x-p-2) Interval is, x = 0 and x = p+3 Given the…

Q: Example 2: Find the area of the region bounded by the curves y=sinx, y-cosx, x-0, and x=2.

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Q: sketch the described regions of integration. -1 ≤ x ≤2, x - 1≤ y ≤ x2

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Q: Example: Determine by integration the area bounded by the three straight lines y=4-x, y=3x and 3y=x

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Q: Sketch the region between y=x^2 +x-2 and the x axis over the interval [-5,2]. Find the area of the…

A: Consider the given equation of the parabola, y=x2+x-2 To draw the graph of the bola first we need to…

Q: 2. Find the area of the region bounded by x- y, x - -1, y = 2 and y = -1. 3. Find the area of the…

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Q: 35. Use integration to find the area of the triangle whose vertices are (0, 0), (1, 3) and (1, 5).

A: To find the area of triangle using integration method

Q: a of the region bounded by y=4x-x^2 and y=x

A: the area bounded by two curves f(x) and g(x) is given by ∫abf(x)-g(x)dx now  y=4x-x2 and y=x2-2x…

Q: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. Show solution and…

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