What is the integral from 3 to 3.5 of 2x^2 ?

The integral from 3 to 3.5 of 2x^2 is 10.58333…

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integral from 3 to 3.5 of 2x^2

\int_{3}^{3.5} 2 x^{2} d x

10.58333 \dots

Solution steps

\int_{3}^{3.5} 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_{3}^{3.5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{3}^{3.5}

= 2 [\frac{x ^{3}}{3}]_{3}^{3.5}

Simplify

= 2 [0.33333 \dots x^{3}]_{3}^{3.5}

Compute the boundaries:

5.29166 \dots

= 2 \cdot 5.29166 \dots

Simplify

= 10.58333 \dots

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What is the integral from 3 to 3.5 of 2x^2 ?
The integral from 3 to 3.5 of 2x^2 is 10.58333…