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Popular >

integral from 0 to 2 of 2x^2-x^3

Solution

\int_{0}^{2} 2 x^{2} - x^{3} d x

Solution

\frac{4}{3}

+1

Decimal Notation

1.33333 \dots

Solution steps

\int_{0}^{2} 2 x^{2} - x^{3} d x

Apply the Sum Rule:

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

= \int_{0}^{2} 2 x^{2} d x - \int_{0}^{2} x^{3} d x

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} x^{3} d x = 4

= \frac{16}{3} - 4

Simplify

\frac{16}{3} - 4 : \frac{4}{3}

= \frac{4}{3}

Popular Examples

derivative of 2x^2+4x+3

\frac{d}{d x} (2 x^{2} + 4 x + 3)

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\int \frac{x - 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

limit as x approaches infinity of (-2)/x

x \to \infty lim (\frac{- 2}{x})

integral of 1/(xsqrt(81-x^2))

\int \frac{1}{x 81 - x ^{2}} d x

integral of 4sin^2(5x+3)+10x^{2/3}-1

\int 4 sin^{2} (5 x + 3) + 10 x^{\frac{2}{3}} - 1 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of 2x^2-x^3 ?
The integral from 0 to 2 of 2x^2-x^3 is 4/3