What is the surface area of the solid created by revolving f ( x ) = 2 x <m

Sattelhofsk

Sattelhofsk

Answered question

2022-06-22

What is the surface area of the solid created by revolving
f ( x ) = 2 x 2 + 3 , x [ 1 , 4 ] around the x axis?

Answer & Explanation

jarakapak7

jarakapak7

Beginner2022-06-23Added 14 answers

The given function: y = 2 x 2 + 3
d y d x = d d x ( 2 x 2 + 3 ) = 4 x
Now, the surface area of solid generated by revolving curve: y = 2 x 2 + 3 around
the x-axis is given by using integration with proper limits
= 2 π y d s
= 0 4 2 π ( 2 x 2 + 3 ) 1 + ( d y d x ) 2 d x
= 2 π 0 4 ( 2 x 2 + 3 ) 1 + ( 4 x ) 2 d x
= 2 π 0 4 ( 2 x 2 + 3 ) 1 + 16 x 2 d x

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