integral from-1 to 3 of cos(sqrt(x+1))

Lösung

\int_{- 1}^{3} cos (x + 1) d x

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

Dezimale

0.80489 \dots

Schritte zur Lösung

\int_{- 1}^{3} cos (x + 1) d x

Wende U-Substitution an

= \int_{0}^{2} cos (u) \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} cos (u) u d u

Wende die partielle Integration an

= 2 [u sin (u) - \int sin (u) d u]_{0}^{2}

\int sin (u) d u = - cos (u)

= 2 [u sin (u) - (- cos (u))]_{0}^{2}

Vereinfache

= 2 [u sin (u) + cos (u)]_{0}^{2}

Berechne die Grenzen:

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

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

\int_{5}^{8} f (2 x) d x

\int_{0}^{l n (2)} x e^{- 4 x} d x

\int_{0}^{9} 4 x d x

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

\int_{- 2}^{x} (16 x^{2} - 15 x) d x