What is the integral from 0 to 0.5 of 8000x ?

The integral from 0 to 0.5 of 8000x is 1000

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integral from 0 to 0.5 of 8000x

\int_{0}^{0.5} 8000 x d x

1000

Solution steps

\int_{0}^{0.5} 8000 x d x

Take the constant out:

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

= 8000 \cdot \int_{0}^{0.5} x d x

Apply the Power Rule

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

= 8000 [\frac{x ^{2}}{2}]_{0}^{0.5}

Simplify

= 8000 [0.5 x^{2}]_{0}^{0.5}

Compute the boundaries:

0.125

= 8000 \cdot 0.125

Simplify

= 1000

n \to \infty lim (\frac{n}{2 n})

y^{^{'}} - x y = x

\int \frac{3 x + 8}{x ( x - 2 ) ^{2}} d x

\frac{d}{d x} (\frac{2 x ^{2} - 1}{3 x + 5})

\frac{d}{d x} (2 x + \frac{2}{x})

What is the integral from 0 to 0.5 of 8000x ?
The integral from 0 to 0.5 of 8000x is 1000