Answer:
[tex]V =\dfrac{25\pi}{\sqrt{2}}[/tex]
Step-by-step explanation:
given,
y=5√sinx
Volume of the solid by revolving
[tex]V = \int_a^b(\pi y^2)dx[/tex]
a and b are the limits of the integrals
now,
[tex]V = \int_a^b(\pi (5\sqrt{sinx})^2)dx[/tex]
[tex]V =25\pi \int_{\pi/4}^{\pi/2}sinxdx[/tex]
[tex]\int sin x = - cos x[/tex]
[tex]V =25\pi [-cos x]_{\pi/4}^{\pi/2}[/tex]
[tex]V =25\pi [-cos (\pi/2)+cos(\pi/4)][/tex]
[tex]V =25\pi [0+\dfrac{1}{\sqrt{2}}][/tex]
[tex]V =\dfrac{25\pi}{\sqrt{2}}[/tex]
volume of the solid generated is equal to [tex]V =\dfrac{25\pi}{\sqrt{2}}[/tex]
