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Popular Cálculo >

integral de-1 a 2 de (3x^2-2x)^3

Solución

\int_{- 1}^{2} (3 x^{2} - 2 x)^{3} d x

Solución

\frac{4836}{35}

+1

Decimal

138.17142 \dots

Pasos de solución

\int_{- 1}^{2} (3 x^{2} - 2 x)^{3} d x

Multiplicar por el conjugado de

3 x^{2} - 2 x : \frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x}

= \int_{- 1}^{2} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x

Encontrar los puntos no definidos (singularidades):

x = 0, x = - \frac{2}{3}

Si existe

b, a < b < c, f (b) =

indefinida

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{- \frac{2}{3}} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x + \int_{- \frac{2}{3}}^{0} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x + \int_{0}^{2} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x

\int_{- 1}^{- \frac{2}{3}} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x = \frac{55844}{2835}

\int_{- \frac{2}{3}}^{0} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x = \frac{6688}{2835}

\int_{0}^{2} (\frac{9 x ^{4} - 4 x ^{2}}{3 x ^{2} + 2 x})^{3} d x = \frac{4064}{35}

= \frac{55844}{2835} + \frac{6688}{2835} + \frac{4064}{35}

Simplificar

\frac{55844}{2835} + \frac{6688}{2835} + \frac{4064}{35} : \frac{4836}{35}

= \frac{4836}{35}

Gráfica

Ejemplos populares

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\int_{2}^{4} sin^{7} (y) d y

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\int_{0}^{\infty} e^{- x} x^{0} d x

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\int_{3}^{7} ln (x) + e^{x} d x

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\int_{1}^{2} y \cdot \frac{2 y}{3} d y