Find the area of the region enclosed by the graphs of the given equations. y = 4

Question

Find the area of the region enclosed by the graphs of the given equations. y = 4-x^2, y = x^2 Additional Materials Use the disk method to find the volume of the solid of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated axis. y = 6x^2, the x-axis, x = 1; about the x-axis Find the volume of the solid of revolution generated by revolving the region shown below about the indicated axis. y = x^2 about the y-axis Use the disk method to find the volume of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated axis. y = 6/root x, the y-axis, y = 12; about the y-axis Use the washer method to find the volume of the solid of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated axis. y = X^2, x > = 0, the y-axis, and y = 4; about the x-axis

Explanation / Answer

7) Area =(4-x^2 - x^2) dx from - sqrt 2 to sqrt2

Area = [4x - x^3/3] from - sqrt2 to sqrt2

Area = 8 sqrt2 - 4 sqrt 2/3 = 20sqrt2 /3 = 9.43 (ans)

8) Volume of revolution = pi*Y^2 dx from x= 0 to 1

V = pi* 36 x^4 dx from x=0 to 1

V = pi*36/5 *x^5 from x=0 to 1

V = pi*36/5= 22.61 unit (ans)

9) Volume = pi*x^2 dy from y= 0 to 4

V = pi*y*dy from y=0 to 4

V = pi*y^2/2 from y=0 to 4

V = 8 pi = 25.12 unit (ans)

10) V = pi * X^2 dy from y=0 to 12

y= 6 sqrtx

x^2 = y^2/36)^2 = y^4/1296

V = pi*y^4/1296 dy from y=0 to 12

V = pi* Y^5/6480 from y=0 to 12

V = 120.58 unit (ans)

11) V = pi*Y2 dx from x=0 to 2

V = pi*x^4 dx from x=0 to2

V = pi*x^5/5 from x=0 to 2

V = 32/5*3.14 = 20.096 unit (ans)

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