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Popular >

integral of |x|^2

Solution

\int ∣ x ∣^{2} d x

Solution

x^{3} - \frac{2 x ^{3}}{3} + C

Solution steps

\int ∣ x ∣^{2} d x

Apply Integration By Parts

: x ∣ x ∣^{2} - \int 2 x^{2} d x

= x ∣ x ∣^{2} - \int 2 x^{2} d x

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

= x ∣ x ∣^{2} - \frac{2 x ^{3}}{3}

x ∣ x ∣^{2} = x^{3}

= x^{3} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= x^{3} - \frac{2 x ^{3}}{3} + C

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Frequently Asked Questions (FAQ)

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