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

The integral from 1 to 4 of 2x^2 is 42

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integral from 1 to 4 of 2x^2

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

42

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= 2 [\frac{x ^{3}}{3}]_{1}^{4}

Compute the boundaries:

21

= 2 \cdot 21

Simplify

= 42

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

What is the integral from 1 to 4 of 2x^2 ?
The integral from 1 to 4 of 2x^2 is 42