$\sin \left(x\right) \cos \left(x\right)\+1\, 0..\frac{\mathrm{\π}}{2}$

$\sin \left(x\right)\cos \left(x\right)\+1\,0..\frac{1}{2}\mathrm{\π}$

$\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolution}\right]\left(\right)$

$\mathrm{\π}\+\frac{9}{16}{\mathrm{\π}}^2$

$\mathrm{evalf}\left(\right)$

$8.693245131$

$\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolution}\right]\left(\, \mathrm{output}\mathit{\=}\mathrm{plot}\mathit{\,}\mathit{ }\mathrm{scaling}\mathit{\=}\mathrm{constrained}\mathit{\,}\mathit{ }\mathrm{caption}\=''''\right)$

$\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolution}\right]\left(\,\mathrm{output}\=\mathrm{integral}\right)$

${\∫}_0^{\frac{1}{2}\mathrm{\π}}\mathrm{\π}{\left(\sin \left(x\right)\cos \left(x\right)\+1\right)}^2\ⅆx$

From the Tools menu, select Tutors, Calculus - Single Variable, and then Volume of Revolution.

Use the following command to launch the tutor:

$\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolutionTutor}\right]\left(\right)$