integral from 2 to sin(x^2) of 1/(1+t^2)

Lösung

\int_{2}^{s i n (x^{2})} \frac{1}{1 + t ^{2}} d t

arctan (sin (x^{2})) - arctan (2)

Schritte zur Lösung

\int_{2}^{s i n (x^{2})} \frac{1}{1 + t ^{2}} d t

Nutze das gemeinsame Integral :

\int \frac{1}{1 + t ^{2}} d t = arctan (t)

= [arctan (t)]_{2}^{s i n (x^{2})}

Berechne die Grenzen:

arctan (sin (x^{2})) - arctan (2)

= arctan (sin (x^{2})) - arctan (2)

\int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} (t) d t

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

\int_{0}^{1} sin (π) t d t

\int_{5}^{6} x (x - 5)^{2} d x

\int_{0}^{1} x 4^{x} d x