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Beliebt Rechnen >

integral from 0 to 16 of sqrt(t^2+2t+1)

Lösung

\int_{0}^{16} t^{2} + 2 t + 1 d t

Lösung

144

Schritte zur Lösung

\int_{0}^{16} t^{2} + 2 t + 1 d t

Faktorisiere

t^{2} + 2 t + 1 : (t + 1)^{2}

= \int_{0}^{16} (t + 1)^{2} d t

Wende Exponentenregel an:

a^{2} = ∣ a ∣

= \int_{0}^{16} (t + 1)^{2} d t

Entferne die Extremwerte

= \int_{0}^{16} (t + 1)^{2} d t

Wende Exponentenregel an:

a^{2} = ∣ a ∣

= \int_{0}^{16} ∣ (t + 1) ∣ d t

Entferne die Extremwerte

= \int_{0}^{16} t + 1 d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{16} t d t + \int_{0}^{16} 1 d t

\int_{0}^{16} t d t = 128

\int_{0}^{16} 1 d t = 16

= 128 + 16

Vereinfache

= 144

Graph

Beliebte Beispiele

y^'=((x^3y^3+4x^3))/(y^2)

y^{^{'}} = \frac{( x ^{3} y ^{3} + 4 x ^{3} )}{y ^{2}}

integral from 1/5 to 3 of 12xln(5x)

\int_{\frac{1}{5}}^{3} 12 x ln (5 x) d x

integral of (x^2+sqrt(x)+1/x)

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

derivative f(x)=5x^2-5x+9

d er i v a t i v e f (x) = 5 x^{2} - 5 x + 9

derivative of-9x^3+27x+7x-66

\frac{d}{d x} (- 9 x^{3} + 27 x + 7 x - 66)