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

The integral from 1 to 2 of 12x^2 is 28

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integral from 1 to 2 of 12x^2

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

28

Solution steps

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{2}

= 12 [\frac{x ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= 12 \cdot \frac{7}{3}

Simplify

= 28

\int_{0}^{3} \frac{x ^{2}}{x ^{3} + 7} d x

\int_{0}^{3} \frac{1}{x ^{3} - x ^{2} - x + 1} d x

\int_{2}^{4} \frac{5}{x} - \frac{10}{x ^{2}} d x

\int_{2}^{5} (cos (\frac{x}{10})) d x

\int_{1}^{- 1} \frac{1}{x ^{2}} d x

What is the integral from 1 to 2 of 12x^2 ?
The integral from 1 to 2 of 12x^2 is 28