integral from 0 to 1 of (1-x^2)sin(x)

Lösung

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

3 - 2 cos (1) - 2 sin (1)

Dezimale

0.23645 \dots

Schritte zur Lösung

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

Multipliziere aus

(1 - x^{2}) sin (x) : sin (x) - x^{2} sin (x)

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

\int_{0}^{1} sin (x) d x = - cos (1) + 1

\int_{0}^{1} x^{2} sin (x) d x = cos (1) + 2 sin (1) - 2

= - cos (1) + 1 - (cos (1) + 2 sin (1) - 2)

Vereinfache

- cos (1) + 1 - (cos (1) + 2 sin (1) - 2) : 3 - 2 cos (1) - 2 sin (1)

= 3 - 2 cos (1) - 2 sin (1)

\int_{1}^{2} 4 x e^{x^{2} + 2} d x

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

\int_{1}^{2} 2 y d y

\int_{- 2}^{3} (2 x^{4} + 4 x^{3} - x + 3) d x

\int_{0}^{6} (36 - x^{2}) d x