calka wsp biegunowe

[aguś_000]

\(\displaystyle{ \int_{0}^{ \pi/4 }d\varphi \int_{sin\varphi}^{cos\varphi} \varrho^3 d\varrho}\)
dochodze do tego iii \(\displaystyle{ \frac{1}{4} \int_{0}^{\pi/4}(cos^4\varphi -sin^4\varphi) d\varphi}\)

[belferkaijuz]

\(\displaystyle{ = \frac{1}{4} \int_{0}^{ \frac{\pi}{4} }(cos^2\varphi-sin^2\varphi)(cos^2\varphi+sin^2\varphi)d\varphi= \frac{1}{4} \int_{0}^{ \frac{\pi}{4} }cos2\varphid\varphi= \frac{1}{4} \cdot (\frac{1}{2}sin2\varphi)|_0^{ \frac{\pi}{4}}\)