integral from 0 to pi/2 of cos(x+y)

Lösung

\int_{0}^{\frac{π}{2}} cos (x + y) d y

sin (x + \frac{π}{2}) - sin (x)

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos (x + y) d y

Wende U-Substitution an

= \int_{x}^{x + \frac{π}{2}} cos (u) d u

Nutze das gemeinsame Integral :

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

= [sin (u)]_{x}^{x + \frac{π}{2}}

Berechne die Grenzen:

sin (x + \frac{π}{2}) - sin (x)

= sin (x + \frac{π}{2}) - sin (x)

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

\int_{0}^{2} e^{t^{2}} d t

\int_{0}^{25} \frac{15}{x} d x

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

\int_{0}^{2} \frac{48}{x ^{2} + 4} d x