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Beliebt Rechnen >

integral from-1 to 1 of pi(7-7x^2)^2

Lösung

\int_{- 1}^{1} π (7 - 7 x^{2})^{2} d x

Lösung

π \frac{784}{15}

+1

Dezimale

164.20057 \dots

Schritte zur Lösung

\int_{- 1}^{1} π (7 - 7 x^{2})^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{- 1}^{1} (7 - 7 x^{2})^{2} d x

Multipliziere aus

(7 - 7 x^{2})^{2} : 49 - 98 x^{2} + 49 x^{4}

= π \cdot \int_{- 1}^{1} 49 - 98 x^{2} + 49 x^{4} 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

= π (\int_{- 1}^{1} 49 d x - \int_{- 1}^{1} 98 x^{2} d x + \int_{- 1}^{1} 49 x^{4} d x)

\int_{- 1}^{1} 49 d x = 98

\int_{- 1}^{1} 98 x^{2} d x = \frac{196}{3}

\int_{- 1}^{1} 49 x^{4} d x = \frac{98}{5}

= π (98 - \frac{196}{3} + \frac{98}{5})

Füge

98 - \frac{196}{3} + \frac{98}{5}

zusammen:

\frac{784}{15}

= π \frac{784}{15}

Graph

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integral of (-x-1)/(x^2+9)

\int \frac{- x - 1}{x ^{2} + 9} d x

(tdy)/(dt)+3y=t^4,t>0,y(1)=3

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tangent f(x)=x^3-3x,(2,2)

t an g e n t f (x) = x^{3} - 3 x, (2, 2)