What is the integral from a to b of a(x) ?

The integral from a to b of a(x) is (a(b^2-a^2))/2

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integral from a to b of a(x)

\int_{a}^{b} a (x) d x

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

Solution steps

\int_{a}^{b} a x d x

Take the constant out:

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

= a \cdot \int_{a}^{b} x d x

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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What is the integral from a to b of a(x) ?
The integral from a to b of a(x) is (a(b^2-a^2))/2