What is the integral from 0 to-0.5 of 150x ?

The integral from 0 to-0.5 of 150x is 18.75

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integral from 0 to-0.5 of 150x

\int_{0}^{- 0.5} 150 x d x

18.75

Solution steps

\int_{0}^{- 0.5} 150 x d x

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

= - \int_{- 0.5}^{0} 150 x d x

Take the constant out:

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

= - 150 \cdot \int_{- 0.5}^{0} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 0.5}^{0}

= - 150 [\frac{x ^{2}}{2}]_{- 0.5}^{0}

Simplify

= - 150 [0.5 x^{2}]_{- 0.5}^{0}

Compute the boundaries:

- 0.125

= - 150 (- 0.125)

Simplify

= 18.75

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What is the integral from 0 to-0.5 of 150x ?
The integral from 0 to-0.5 of 150x is 18.75