What is the integral from a to b of 3x^2 ?

The integral from a to b of 3x^2 is b^3-a^3

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integral from a to b of 3x^2

\int_{a}^{b} 3 x^{2} d x

b^{3} - a^{3}

Solution steps

\int_{a}^{b} 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int_{a}^{b} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{a}^{b}

= 3 [\frac{x ^{3}}{3}]_{a}^{b}

Compute the boundaries:

\frac{b ^{3}}{3} - \frac{a ^{3}}{3}

= 3 (\frac{b ^{3}}{3} - \frac{a ^{3}}{3})

Simplify

= b^{3} - a^{3}

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What is the integral from a to b of 3x^2 ?
The integral from a to b of 3x^2 is b^3-a^3