What is the integral from 0 to h of (kx+v) ?

The integral from 0 to h of (kx+v) is hv+(h^2k)/2

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integral from 0 to h of (kx+v)

\int_{0}^{h} (k x + v) d x

h v + \frac{h ^{2} k}{2}

Solution steps

\int_{0}^{h} k x + v d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{h} v d x + \int_{0}^{h} k x d x

\int_{0}^{h} v d x = h v

\int_{0}^{h} k x d x = \frac{h ^{2} k}{2}

= h v + \frac{h ^{2} k}{2}

What is the integral from 0 to h of (kx+v) ?
The integral from 0 to h of (kx+v) is hv+(h^2k)/2