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Popular >

integral from 0 to 8 of t(8-t)

Solution

\int_{0}^{8} t (8 - t) d t

Solution

\frac{256}{3}

+1

Decimal Notation

85.33333 \dots

Solution steps

\int_{0}^{8} t (8 - t) d t

Expand

t (8 - t) : 8 t - t^{2}

= \int_{0}^{8} 8 t - t^{2} d t

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}^{8} 8 t d t - \int_{0}^{8} t^{2} d t

\int_{0}^{8} 8 t d t = 256

\int_{0}^{8} t^{2} d t = \frac{512}{3}

= 256 - \frac{512}{3}

Simplify

256 - \frac{512}{3} : \frac{256}{3}

= \frac{256}{3}

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\int_{0}^{2} e^{x} + \frac{1}{x ^{2} + 1} d x

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\int_{1}^{2} e^{- l n (x)} d x

integral from 4 to 13 of 1/(sqrt(x-4))

\int_{4}^{13} \frac{1}{x - 4} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of t(8-t) ?
The integral from 0 to 8 of t(8-t) is 256/3