What is the integral from a to 10b of 2s ?

The integral from a to 10b of 2s is 100b^2-a^2

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integral from a to 10b of 2s

\int_{a}^{10 b} 2 s d s

100 b^{2} - a^{2}

Solution steps

\int_{a}^{10 b} 2 s d s

Take the constant out:

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

= 2 \cdot \int_{a}^{10 b} s d s

Apply the Power Rule

: [\frac{s ^{2}}{2}]_{a}^{10 b}

= 2 [\frac{s ^{2}}{2}]_{a}^{10 b}

Compute the boundaries:

50 b^{2} - \frac{a ^{2}}{2}

= 2 (50 b^{2} - \frac{a ^{2}}{2})

Simplify

= 100 b^{2} - a^{2}

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What is the integral from a to 10b of 2s ?
The integral from a to 10b of 2s is 100b^2-a^2