What is the integral from a to x of x ?

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

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integral from a to x of x

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

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

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

= \frac{x ^{2}}{2} - \frac{a ^{2}}{2}

Simplify

= \frac{x ^{2} - a ^{2}}{2}

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