What is the integral of 30(25-t^2) ?

The integral of 30(25-t^2) is 30(25t-(t^3)/3)+C

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integral of 30(25-t^2)

\int 30 (25 - t^{2}) d t

30 (25 t - \frac{t ^{3}}{3}) + C

Solution steps

\int 30 (25 - t^{2}) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 30 \cdot \int 25 - 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

= 30 (\int 25 d t - \int t^{2} d t)

\int 25 d t = 25 t

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

= 30 (25 t - \frac{t ^{3}}{3})

Add a constant to the solution

= 30 (25 t - \frac{t ^{3}}{3}) + C

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What is the integral of 30(25-t^2) ?
The integral of 30(25-t^2) is 30(25t-(t^3)/3)+C