integral from 0 to pi/2 of-4cos(t)sin(t)

Lösung

\int_{0}^{\frac{π}{2}} - 4 cos (t) sin (t) d t

- 2

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} - 4 cos (t) sin (t) d t

Entferne die Konstante:

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

= - 4 \cdot \int_{0}^{\frac{π}{2}} cos (t) sin (t) d t

Wende U-Substitution an

= - 4 \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= - 4 [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= - 4 \cdot \frac{1}{2}

Vereinfache

= - 2

\int_{0}^{1} 1 + x^{3} x^{2} d x

\int_{0}^{1} x^{2} - 2 x + 8 d x

\int_{1}^{2} \frac{e ^{x}}{x ^{2}} d x

\int_{0}^{t} x^{2} - 3 x + 2 d x

\int_{0}^{1} 2 - x - y d y