What is the integral from 0 to 50 of t/(w-20) ?

The integral from 0 to 50 of t/(w-20) is (1250)/(-20+w)

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integral from 0 to 50 of t/(w-20)

\int_{0}^{50} \frac{t}{w - 20} d t

\frac{1250}{- 20 + w}

Solution steps

\int_{0}^{50} \frac{t}{w - 20} d t

Take the constant out:

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

= \frac{1}{- 20 + w} \cdot \int_{0}^{50} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{50}

= \frac{1}{- 20 + w} [\frac{t ^{2}}{2}]_{0}^{50}

Simplify

\frac{1}{- 20 + w} [\frac{t ^{2}}{2}]_{0}^{50} : \frac{[ \frac{t ^{2}}{2} ] _{0}^{50}}{- 20 + w}

= \frac{[ \frac{t ^{2}}{2} ] _{0}^{50}}{- 20 + w}

Compute the boundaries:

1250

= \frac{1250}{- 20 + w}

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What is the integral from 0 to 50 of t/(w-20) ?
The integral from 0 to 50 of t/(w-20) is (1250)/(-20+w)