What is the integral from 1 to 4 of 12x^2 ?

The integral from 1 to 4 of 12x^2 is 252

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integral from 1 to 4 of 12x^2

\int_{1}^{4} 12 x^{2} d x

252

Solution steps

\int_{1}^{4} 12 x^{2} d x

Take the constant out:

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

= 12 \cdot \int_{1}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{4}

= 12 [\frac{x ^{3}}{3}]_{1}^{4}

Compute the boundaries:

21

= 12 \cdot 21

Simplify

= 252

\int_{0}^{4} \frac{1}{4} x^{2} d x

\int_{0}^{3} (x - 8)^{2} d x

\int_{2}^{6} - x^{2} + 8 x - 12 d x

\int_{1}^{2} (x^{2} + 2 x + 1) d x

\int_{2}^{6} x (x^{2} + 7) d x

What is the integral from 1 to 4 of 12x^2 ?
The integral from 1 to 4 of 12x^2 is 252