What is the integral of pi(x^2-x^4) ?

The integral of pi(x^2-x^4) is pi((x^3)/3-(x^5)/5)+C

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integral of pi(x^2-x^4)

\int π (x^{2} - x^{4}) d x

π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5}) + C

Solution steps

\int π (x^{2} - x^{4}) d x

Take the constant out:

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

= π \cdot \int x^{2} - x^{4} d x

Apply the Sum Rule:

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

= π (\int x^{2} d x - \int x^{4} d x)

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

\int x^{4} d x = \frac{x ^{5}}{5}

= π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5})

Add a constant to the solution

= π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5}) + C

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What is the integral of pi(x^2-x^4) ?
The integral of pi(x^2-x^4) is pi((x^3)/3-(x^5)/5)+C