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Popular >

integral of (4-r^2)r

Solution

\int (4 - r^{2}) r d r

Solution

2 r^{2} - \frac{r ^{4}}{4} + C

Solution steps

\int (4 - r^{2}) r d r

Expand

(4 - r^{2}) r : 4 r - r^{3}

= \int 4 r - r^{3} d r

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 r d r - \int r^{3} d r

\int 4 r d r = 2 r^{2}

\int r^{3} d r = \frac{r ^{4}}{4}

= 2 r^{2} - \frac{r ^{4}}{4}

Add a constant to the solution

= 2 r^{2} - \frac{r ^{4}}{4} + C

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n \to \infty lim (n^{n})

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\int 2^{2 x} d x

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\frac{d}{d x} (- \frac{24}{x ^{4}})

Frequently Asked Questions (FAQ)

What is the integral of (4-r^2)r ?
The integral of (4-r^2)r is 2r^2-(r^4)/4+C