a Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. b Use your calculator to evaluate the integral correct to five decimal places. y=sinx,y=0,x=2,x=3;aboutthey-axis
The integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.
i. If is the radius of the typical shell, then the circumference and the height is
ii. By the shell method, the volume of the solid by rotating the region under the curve about from to is
, rotate about
As the region is bounded by , and rotated about , draw the region using the given curves.
The graph shows the region. A typical cylindrical shell formed by rotation about the line has the radius .
Therefore, the circumference is and the height is
It is given that
So, the volume of the given solid is
The integral for the volume of the solid obtained by rotating the region bounded by the given curves about the is
The integral ofthe volume of the solid
Use calculator of integration to evaluate integral
From part (a)
Evaluate the integral by using a calculator Ti-84 plus.
Use the below steps:
1) Click on “Math” option.
2) After that under “Math” search for the option “fnInt(“
3) Write the lower limit, upper limit and function using the proper brackets and required variable.
4) Press enter key; it will display the final answer.