Question

Integrala de la 0la pi/2 sinxcosx dx integrala prin parti

Answer 1

[tex] \int\limits^{\pi / 2}_0 {\sin x \cos x} \, dx = \int\limits^{\pi / 2}_0 {\sin x (\sin x)'} \, dx = \left. \sin^2 x\,\right|_0^{\pi / 2}- \underset{I}{\underbrace{\int\limits^{\pi / 2}_0 {\cos x \sin x} \, dx }} \Rightarrow 2I = \left. \sin^2 x\,\right|_0^{\pi / 2} = 1 \Rightarrow I = \frac{1}{2}[/tex]