integral from 1 to 6 of sin(4x+2.8)

Lösung

\int_{1}^{6} sin (4 x + 2.8) d x

0.24142 \dots

Schritte zur Lösung

\int_{1}^{6} sin (4 x + 2.8) d x

Wende U-Substitution an

= \int_{6.8}^{26.8} sin (u) \frac{1}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{6.8}^{26.8} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [- cos (u)]_{6.8}^{26.8}

Vereinfache

= 0.25 [- cos (u)]_{6.8}^{26.8}

Berechne die Grenzen:

0.96571 \dots

= 0.25 \cdot 0.96571 \dots

Vereinfache

= 0.24142 \dots

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

\int_{0}^{b} \frac{7 x}{8} d x

\int_{1}^{t} \frac{1}{( 2 x + 1 ) ^{3}} d x

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

\int_{0}^{3} 4 r^{2} + 1 r d r