Question

1) Find the volume of the solid obtained by rotating the region enclosed by the graphs about the given axis. ?=2?^(1/2), y=x about y=6 (Use symbolic notation and fractions where needed.)

2) Find the volume of a solid obtained by rotating the region enclosed by the graphs of ?=?^(−?), y=1−e^(−x), and x=0 about y=4.5.

(Use symbolic notation and fractions where needed.)

Answer #1

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 5x4, y = 5x, x ≥
0; about the x-axis
Find the area of the region enclosed by the given curves.
y = 3 cos(πx), y = 12x2 −
3
Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
2x = y2, x = 0, y =
5; about the...

1- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
?= 64x− 8x^2, y=0;
about the y-axis
2- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y= 5+ 1/x^2, y= 5, x=2, x=9;
about the x-axis.

Find the volume of the solid formed by rotating the region
enclosed by
y=e^2x +5 , y=0, x=0, x=1, about the x axis.

Find the volume V of the solid obtained by rotating the region
bounded by the given curves about the specified line. y = x − 1 , y
= 0, x = 6; about the x-axis

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis. y = x 2 , y =
1 about y = 6.

(1 point) Find the volume of the solid obtained by rotating the
region bounded by the given curves about the specified axis. x+y=2,
x = 3-(y-1)^2 ; about the x-axis.

find the volume of the solid obtained by rotating the region R
enclosed by the curves y = x^2 and y = 2x.
1. rotated around the x-axiz a. 8pi/3 b. 16pi/3 c. 32pi/15 d.
64pi/15 e. none of the above
2. around the y-axis (with same multiple choice answers as a
bove)
3. around line x=2 (with the same choice answers as question
1)

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y=0,y=cos(4x), x= π/8, x=0 about the axis y=−2

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y=0, y=cos(2x), x=π/4, x=0 about the axis y=−1

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line.
a) y = sin x − 2(x − 1)2 + 2(π − 1)2 , y =
0, about the x axis.

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