What is the integral from 1 to 5 of 2x^2 ?

The integral from 1 to 5 of 2x^2 is 248/3

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integral from 1 to 5 of 2x^2

\int_{1}^{5} 2 x^{2} d x

\frac{248}{3}

Decimal

82.66666 \dots

Solution steps

\int_{1}^{5} 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}^{5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{5}

= 2 [\frac{x ^{3}}{3}]_{1}^{5}

Compute the boundaries:

\frac{124}{3}

= 2 \cdot \frac{124}{3}

Simplify

= \frac{248}{3}

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What is the integral from 1 to 5 of 2x^2 ?
The integral from 1 to 5 of 2x^2 is 248/3