What is the integral from 0 to-2.5 of 100x ?

The integral from 0 to-2.5 of 100x is 312.5

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integral from 0 to-2.5 of 100x

\int_{0}^{- 2.5} 100 x d x

312.5

Solution steps

\int_{0}^{- 2.5} 100 x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2.5}^{0} 100 x d x

Take the constant out:

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

= - 100 \cdot \int_{- 2.5}^{0} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 2.5}^{0}

= - 100 [\frac{x ^{2}}{2}]_{- 2.5}^{0}

Simplify

= - 100 [0.5 x^{2}]_{- 2.5}^{0}

Compute the boundaries:

- 3.125

= - 100 (- 3.125)

Simplify

= 312.5

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What is the integral from 0 to-2.5 of 100x ?
The integral from 0 to-2.5 of 100x is 312.5