What is the integral from 0 to 3 of-12x ?

The integral from 0 to 3 of-12x is -54

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integral from 0 to 3 of-12x

\int_{0}^{3} - 12 x d x

- 54

Solution steps

\int_{0}^{3} - 12 x d x

Take the constant out:

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

= - 12 \cdot \int_{0}^{3} x d x

Apply the Power Rule

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

= - 12 [\frac{x ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

= - 12 \cdot \frac{9}{2}

Simplify

= - 54

\int_{- 2}^{0} 3 x^{3} - 12 x d x

\int_{0}^{4} (x^{2} + 6 x) d x

\int_{- 0.5}^{0} b + 2 b x d x

\int_{- 1}^{1} (x^{5} - 4 x^{2} + x - 1) d x

\int_{0}^{1} t^{2} + t d t

What is the integral from 0 to 3 of-12x ?
The integral from 0 to 3 of-12x is -54