Calculate the area of the region bounded by y=6x and y=6x^2. And find the volume of the solid generated by revolving the region about the x-axis

Hence, the Area is

Step-by-step explanation:

Concept :

Area of the region bounded by two curve :

volume of the solid generated by revolving the region about the x-axis is :

    where is long radius of bounded region from x-axis and is short radius of bounded region from x-axis.

Given :

and

To find :

Area of the region bounded by and and volume of the solid generated by revolving the region about the x-axis.

Explanation :

Area of the region bounded by and is :

Volume of the solid generated by revolving the region about the x-axis.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2