integral from 0 to pi/4 of sin(x)+cos(x)

Lösung

\int_{0}^{\frac{π}{4}} sin (x) + cos (x) d x

1

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} sin (x) + cos (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}{4}} sin (x) d x + \int_{0}^{\frac{π}{4}} cos (x) d x

\int_{0}^{\frac{π}{4}} sin (x) d x = - \frac{1}{2} + 1

\int_{0}^{\frac{π}{4}} cos (x) d x = \frac{1}{2}

= - \frac{1}{2} + 1 + \frac{1}{2}

Vereinfache

= 1

\int_{6}^{8} \frac{x}{50} d x

\int_{4}^{16} \frac{x}{2} - x d x

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