∫ #160; _ r ^ 3 ( 3 x^ 2 ) #160; dx = ∫ #160; _ r ^ 3 ( 3 x^ 2 ) dx =3∫ #160; _ r ^ 3 ( x ) #160; ^ 2 dx =3∫ #160; _ r ^ ...

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Functions

Integrate: ∫...

Question

Integrate:
$\int_{r}^{3} (3 x^{2}) d x$

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Solution

$\int_{r}^{3} (3 x^{2}) d x = \int_{r}^{3} (3 x^{2}) d x = 3 \int_{r}^{3} {(x)}^{2} d x = 3 \int_{r}^{3} \frac{x^{3}}{3} = {[x^{3} + x + c]}_{r}^{3} = (3^{3} + 3 + c) - (r^{3} + r + c) = 27 + 3 + c - r^{3} - r + c = - r^{3} - r + 30$

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