integral from 0 to pi/2 of (6+3sin(x))

Lösung

\int_{0}^{\frac{π}{2}} (6 + 3 sin (x)) d x

3 π + 3

Dezimale

12.42477 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 6 + 3 sin (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{2}} 6 d x + \int_{0}^{\frac{π}{2}} 3 sin (x) d x

\int_{0}^{\frac{π}{2}} 6 d x = 3 π

\int_{0}^{\frac{π}{2}} 3 sin (x) d x = 3

= 3 π + 3

\int_{0}^{3} x sin (\frac{mπ x}{3}) d x

\int_{4}^{6} \frac{1}{x ^{2} - 25} d x

\int_{0}^{\frac{π}{14}} sin^{5} (7 x) d x

\int_{11}^{\infty} \frac{1}{x ^{6}} d x

\int_{π - α}^{2 π} - 1