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Popular >

integral of t(t-2)

Solution

\int t (t - 2) d t

Solution

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

Solution steps

\int t (t - 2) d t

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

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\frac{d}{d x} (\frac{x + 2}{x + 1})

Frequently Asked Questions (FAQ)

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