What is the integral from 0 to 1 of (3t^2-4t^3) ?

The integral from 0 to 1 of (3t^2-4t^3) is 0

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integral from 0 to 1 of (3t^2-4t^3)

\int_{0}^{1} (3 t^{2} - 4 t^{3}) d t

0

Solution steps

\int_{0}^{1} 3 t^{2} - 4 t^{3} 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}^{1} 3 t^{2} d t - \int_{0}^{1} 4 t^{3} d t

\int_{0}^{1} 3 t^{2} d t = 1

\int_{0}^{1} 4 t^{3} d t = 1

= 1 - 1

Simplify

= 0

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What is the integral from 0 to 1 of (3t^2-4t^3) ?
The integral from 0 to 1 of (3t^2-4t^3) is 0