How do you find the volume of the solid obtained by rotating the region bounded by the curves Y=2x a

telegrafyx

telegrafyx

Answered question

2022-06-21

How do you find the volume of the solid obtained by rotating the region bounded by the curves Y=2x and Y = x 2 rotated around the x-axis?

Answer & Explanation

Rebekah Zimmerman

Rebekah Zimmerman

Beginner2022-06-22Added 32 answers

Remembering that the area between f(x) and g(x), with f(x) over g(x) from x 1 to x 2 is given by:
x 1 x 2 [ f ( x ) g ( x ) ] d x ,
and since y=2x is over the function y = x 2 , and the intercept point is given by the system:
y=2x
y = x 2
2 x = x 2 x ( x 2 ) = 0
x 1 = 0 and x 2 = 2,
then
0 1 ( 2 x x 2 ) d x = [ x 2 x 3 3 ] 0 2 =
= [ 2 2 2 3 3 ( 0 2 0 3 3 ) ] = 4 8 3 = 4 3

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