What is the integral from 0 to 4 of-50(t-10) ?

The integral from 0 to 4 of-50(t-10) is 1600

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integral from 0 to 4 of-50(t-10)

\int_{0}^{4} - 50 (t - 10) d t

1600

Solution steps

\int_{0}^{4} - 50 (t - 10) d t

Take the constant out:

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

= - 50 \cdot \int_{0}^{4} t - 10 d t

Apply the Sum Rule:

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

= - 50 (\int_{0}^{4} t d t - \int_{0}^{4} 10 d t)

\int_{0}^{4} t d t = 8

\int_{0}^{4} 10 d t = 40

= - 50 (8 - 40)

Simplify

= 1600

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What is the integral from 0 to 4 of-50(t-10) ?
The integral from 0 to 4 of-50(t-10) is 1600