What is the integral from a to sqrt(3a of)x ?

The integral from a to sqrt(3a of)x is (3a-a^2)/2

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integral from a to sqrt(3a of)x

\int_{a}^{3 a} x d x

\frac{3 a - a ^{2}}{2}

Solution steps

\int_{a}^{3 a} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{a}^{3 a}

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

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

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

Compute the boundaries:

\frac{3 a}{2} - \frac{a ^{2}}{2}

= \frac{3 a}{2} - \frac{a ^{2}}{2}

Simplify

= \frac{3 a - a ^{2}}{2}

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What is the integral from a to sqrt(3a of)x ?
The integral from a to sqrt(3a of)x is (3a-a^2)/2