What is the integral from 0 to 0.5 of 625x ?

The integral from 0 to 0.5 of 625x is 78.125

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integral from 0 to 0.5 of 625x

\int_{0}^{0.5} 625 x d x

78.125

Solution steps

\int_{0}^{0.5} 625 x d x

Take the constant out:

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

= 625 \cdot \int_{0}^{0.5} x d x

Apply the Power Rule

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

= 625 [\frac{x ^{2}}{2}]_{0}^{0.5}

Simplify

= 625 [0.5 x^{2}]_{0}^{0.5}

Compute the boundaries:

0.125

= 625 \cdot 0.125

Simplify

= 78.125

f (x) = x 3^{x}

(sin^{2} (3 x))^{^{'}}

\int \frac{5 - 50 x}{9 - 25 x ^{2}} d x

\frac{d}{d x} (3 x sin (x^{2}))

What is the integral from 0 to 0.5 of 625x ?
The integral from 0 to 0.5 of 625x is 78.125