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Popular >

integral from 0 to 4 of t(4-t)

Solution

\int_{0}^{4} t (4 - t) d t

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

\int_{0}^{4} t (4 - t) d t

Expand

t (4 - t) : 4 t - t^{2}

= \int_{0}^{4} 4 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}^{4} 4 t d t - \int_{0}^{4} t^{2} d t

\int_{0}^{4} 4 t d t = 32

\int_{0}^{4} t^{2} d t = \frac{64}{3}

= 32 - \frac{64}{3}

Simplify

32 - \frac{64}{3} : \frac{32}{3}

= \frac{32}{3}

Graph

Popular Examples

integral from 0 to 1 of 2x-x^2-x^3

\int_{0}^{1} 2 x - x^{2} - x^{3} d x

integral from-1 to 4 of 2x+1

\int_{- 1}^{4} 2 x + 1 d x

integral from 0 to 1 of x^2+x+1

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

integral from 0 to 3 of e^{x/3}

\int_{0}^{3} e^{\frac{x}{3}} d x

integral from 0 to pi of (cos(x))^3

\int_{0}^{π} (cos (x))^{3} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of t(4-t) ?
The integral from 0 to 4 of t(4-t) is 32/3