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Beliebt Rechnen >

integral from 0 to 5/4 of 1/(25+16x^2)

Lösung

\int_{0}^{\frac{5}{4}} \frac{1}{25 + 16 x ^{2}} d x

Lösung

\frac{π}{80}

+1

Dezimale

0.03926 \dots

Schritte zur Lösung

\int_{0}^{\frac{5}{4}} \frac{1}{25 + 16 x ^{2}} d x

Wende integrale Substitution an

= \int_{0}^{1} \frac{1}{20 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{20} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{20} [arctan (u)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{20} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{80}

Graph

Beliebte Beispiele

derivative of yln(x)

\frac{d}{d x} (y ln (x))

tangent 6cos(t),\at t=-pi/4

t an g e n t 6 cos (t), at t = - \frac{π}{4}

inverselaplace 2s+1

in v erse l a pl a ce 2 s + 1

tangent f(x)=x^4-4x^3+2x^2-6,\at x=1

t an g e n t f (x) = x^{4} - 4 x^{3} + 2 x^{2} - 6, at x = 1

integral of (x^2)/(x^2+x+12)

\int \frac{x ^{2}}{x ^{2} + x + 12} d x