Question

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

Answer #1

We can use disk method

bound is from 1 to 6

now, we can set up integral

now, we can solve it

now, we can solve each integrals

and then combine them

and we get

**..............Answer**

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...

Find the volume V of the solid obtained by rotating the region
bounded by the given curves about the specified line. 2x = y^2, x =
0, y = 5; about the y-axis
sketch the region, sketch the solid

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = ln(5x), y = 2, y = 5, x =
0; about the y-axis

Find the volume V of the solid obtained by rotating the region
bounded by the given curves about the specified line.
X = 4
X = √y , x =0 , y = 3x + 6

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
X=4
X = squroot(y) , x =0 , y = 3x + 6

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 V of the solid obtained by rotating the region
bounded by the given curves about the specified line. y = 5 sin(x),
y = 5 cos(x), 0 ≤ x ≤ π/4; about y = −1

find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. y=sqrt x-4 ,
y=0 and x=9 rotated 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 = 2 + sec(x),
−π
3
≤ x ≤
π
3
, y = 4; about
y = 2
V =
Sketch the region.
Sketch the solid, and a typical disk or washer.

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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