Find the volume v obtained by rotating the region bounded by the curves about the given axis.
y = 3 sin2(x), y = 0, 0 ≤ x ≤ π; about the x−axis

Use Disc-method here:


The radius of each circle cross-section is equal to the y-value of function.
The limits are from 0 to pi.



Integrate by using trig identities to transform sin^4.


Sub back into integral:
 

1. 0.3 •4 is the same as 4 groups of 0.32. 7•0.8 is the same as 7 groups of 0.83. it increases by 0.5 every time, so 0.5x4 it increases by 0.9 every time, so 0.9x5. 0.9•12=10.86. 0.47•5=2.35i can finish the next ones in a separate post