integral from 0 to cos(x) of ysin(x)

Lösung

\int_{0}^{c o s (x)} y sin (x) d y

\frac{cos ^{2} ( x ) sin ( x )}{2}

Schritte zur Lösung

\int_{0}^{c o s (x)} y sin (x) d y

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sin (x) \cdot \int_{0}^{c o s (x)} y d y

Wende die Potenzregel an

= sin (x) [\frac{y ^{2}}{2}]_{0}^{c o s (x)}

Berechne die Grenzen:

\frac{cos ^{2} ( x )}{2}

= sin (x) \frac{cos ^{2} ( x )}{2}

Vereinfache

= \frac{cos ^{2} ( x ) sin ( x )}{2}

\int_{0}^{7} (2 x x^{2} - 1) d x

\int_{\frac{π}{3}}^{\frac{π}{6}} tan^{2} (x) d x

\int_{- 1}^{3} e^{x} - 3 d x

\int_{0}^{1} (1 - e^{2})^{\frac{1}{2}} d x

\int_{0}^{2} (\frac{1}{1 + x ^{2}})^{2} d x