Beräkna bestämd integral

Uppgift:  Beräkna ${\int }_0^{\frac{\pi }{2} }{x}^2\cos \left(2x\right) dx$

$\int x^2\cos \left(2x\right) = x^2\sin \left(x\right)\cos \left(x\right) - \frac{1}{4}\sin \left(2x\right) +\frac{1}{2}x\cos \left(2x\right)$

$x^2\sin \left(x\right)\cos \left(x\right){\parallel }_0^{\mathrm{\pi }/2} =(\hspace{0.17em}\frac{\mathrm{\pi }}{2}{)}^2\sin (\frac{\mathrm{\pi }}{2}\left)\cos \right(\frac{\mathrm{\pi }}{2}) - 0 = 0$

$\frac{1}{4}\sin (2x{)}_0^{\frac{\mathrm{\pi }}{2}}=\frac{1}{4}\sin (\frac{2\mathrm{\pi }}{2}) -\frac{1}{4}\sin (2*0) = 0$

$\frac{1}{2}x\cos (2x{)}_0^{\frac{\mathrm{\pi }}{2}} = \frac{1}{2}\frac{\mathrm{\pi }}{2}\cos (\mathrm{\pi }) -\frac{1}{2}0*\cos (0) =-\frac{\mathrm{\pi }}{4}$

Svar: 0 + 0  - π/4 = -π/4