What is the integral from 0 to-0.4 of 400x ?

The integral from 0 to-0.4 of 400x is 32

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integral from 0 to-0.4 of 400x

\int_{0}^{- 0.4} 400 x d x

32

Solution steps

\int_{0}^{- 0.4} 400 x d x

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

= - \int_{- 0.4}^{0} 400 x d x

Take the constant out:

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

= - 400 \cdot \int_{- 0.4}^{0} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 0.4}^{0}

= - 400 [\frac{x ^{2}}{2}]_{- 0.4}^{0}

Simplify

= - 400 [0.5 x^{2}]_{- 0.4}^{0}

Compute the boundaries:

- 0.08

= - 400 (- 0.08)

Simplify

= 32

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What is the integral from 0 to-0.4 of 400x ?
The integral from 0 to-0.4 of 400x is 32