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Popular >

integral of 1/3 x^2

Solution

\int \frac{1}{3} x^{2} d x

Solution

\frac{x ^{3}}{9} + C

Solution steps

\int \frac{1}{3} x^{2} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{3} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{3} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{9}

= \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{x ^{3}}{9} + C

Popular Examples

limit as x approaches 0 of x^3+x

x \to 0 lim (x^{3} + x)

integral of 2/((x^2+1)^{3/2)}

\int \frac{2}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

derivative of sqrt((1-3x/(2x+1)))

\frac{d}{d x} (\frac{1 - 3 x}{2 x + 1})

limit as x approaches pi/6 of sin(x)

x \to \frac{π}{6} lim (sin (x))

integral of 8xln(5x)

\int 8 x ln (5 x) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/3 x^2 ?
The integral of 1/3 x^2 is (x^3)/9+C