integral from 1 to 2 of x^2+1/(4x^2)

Lösung

\int_{1}^{2} x^{2} + \frac{1}{4 x ^{2}} d x

\frac{59}{24}

Dezimale

2.45833 \dots

Schritte zur Lösung

\int_{1}^{2} x^{2} + \frac{1}{4 x ^{2}} 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_{1}^{2} x^{2} d x + \int_{1}^{2} \frac{1}{4 x ^{2}} d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{4 x ^{2}} d x = \frac{1}{8}

= \frac{7}{3} + \frac{1}{8}

Vereinfache

\frac{7}{3} + \frac{1}{8} : \frac{59}{24}

= \frac{59}{24}

f (x) = 1 - e^{- x}

\int \frac{4}{9 - 9 x ^{2}} d x

\frac{d}{d x} (15 x^{5} - \frac{60}{7 x ^{6}} - 1)

\int \frac{r}{( r ^{2} + z ^{2} ) ^{\frac{3}{2}}} d r

\frac{d}{d x} (\frac{- 4 x}{x ^{4} - 2 x ^{2} + 1})