What is the integral from 0 to 5 of 6x ?

The integral from 0 to 5 of 6x is 75

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integral from 0 to 5 of 6x

\int_{0}^{5} 6 x d x

75

Solution steps

\int_{0}^{5} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{0}^{5} x d x

Apply the Power Rule

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

= 6 [\frac{x ^{2}}{2}]_{0}^{5}

Compute the boundaries:

\frac{25}{2}

= 6 \cdot \frac{25}{2}

Simplify

= 75

\int_{8}^{1} 0.2 x^{2} + 1 d x

\int_{2}^{5} 5^{2 x} d x

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\int_{6}^{12} \frac{36}{x} d x

\int_{- 1}^{2} (5 - 2 x) d x