What is the integral from 0 to 3 of 5x ?

The integral from 0 to 3 of 5x is 45/2

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integral from 0 to 3 of 5x

\int_{0}^{3} 5 x d x

\frac{45}{2}

Decimal Notation

22.5

Solution steps

\int_{0}^{3} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{0}^{3} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{3}

= 5 [\frac{x ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

= 5 \cdot \frac{9}{2}

Simplify

= \frac{45}{2}

\int \frac{1}{x ^{2} - 64} d x

x \to - 2 lim (8 + 1^{3})

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

\frac{d y}{d x} = \frac{x + y}{y - x}

f (x) = 10 x^{3} - 45 x^{2} + 60 x - 30