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Popular >

integral from 4 to 6 of 4x-x^2

Solution

\int_{4}^{6} 4 x - x^{2} d x

Solution

- \frac{32}{3}

+1

Decimal Notation

- 10.66666 \dots

Solution steps

\int_{4}^{6} 4 x - x^{2} 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_{4}^{6} 4 x d x - \int_{4}^{6} x^{2} d x

\int_{4}^{6} 4 x d x = 40

\int_{4}^{6} x^{2} d x = \frac{152}{3}

= 40 - \frac{152}{3}

Simplify

40 - \frac{152}{3} : - \frac{32}{3}

= - \frac{32}{3}

Popular Examples

integral from 0 to 2 of 3x^2e^{-2x}

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

integral from e to e^3 of (4(ln(x))^3)/x

\int_{e}^{e^{3}} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

integral from a to r of r^2

\int_{a}^{r} r^{2} d r

integral from 11 to infinity of 1/(x^2)

\int_{11}^{\infty} \frac{1}{x ^{2}} d x

integral from 0 to pi/3 of (9x-2)cos(3x)

\int_{0}^{\frac{π}{3}} (9 x - 2) cos (3 x) d x

Frequently Asked Questions (FAQ)

What is the integral from 4 to 6 of 4x-x^2 ?
The integral from 4 to 6 of 4x-x^2 is -32/3