What is the integral from v^1 to v^2 of v ?

The integral from v^1 to v^2 of v is (v^4-v^2)/2

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integral from v^1 to v^2 of v

\int_{v^{1}}^{v^{2}} v d v

\frac{v ^{4} - v ^{2}}{2}

Solution steps

\int_{v^{1}}^{v^{2}} v d v

Apply the Power Rule

= [\frac{v ^{2}}{2}]_{v^{1}}^{v^{2}}

Simplify

= [\frac{v ^{2}}{2}]_{v}^{v^{2}}

Compute the boundaries:

\frac{v ^{4}}{2} - \frac{v ^{2}}{2}

= \frac{v ^{4}}{2} - \frac{v ^{2}}{2}

Simplify

= \frac{v ^{4} - v ^{2}}{2}

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What is the integral from v^1 to v^2 of v ?
The integral from v^1 to v^2 of v is (v^4-v^2)/2