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Popular Calculus >

integral of t(1-t)

Solution

integral

t (1 - t)

Solution

\frac{t ^{2}}{2} - \frac{t ^{3}}{3} + C

Solution steps

\int t (1 - t) d t

Expand

t (1 - t) : t - t^{2}

= \int 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 t d t - \int t^{2} d t

\int t d t = \frac{t ^{2}}{2}

\int t^{2} d t = \frac{t ^{3}}{3}

= \frac{t ^{2}}{2} - \frac{t ^{3}}{3}

Add a constant to the solution

= \frac{t ^{2}}{2} - \frac{t ^{3}}{3} + C

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the integral of t(1-t) ?
The integral of t(1-t) is (t^2)/2-(t^3)/3+C