What is the integral from 1 to 0 of 3x ?

The integral from 1 to 0 of 3x is -3/2

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integral from 1 to 0 of 3x

\int_{1}^{0} 3 x d x

- \frac{3}{2}

Decimal

- 1.5

Solution steps

\int_{1}^{0} 3 x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} 3 x d x

Take the constant out:

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

= - 3 \cdot \int_{0}^{1} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{1}

= - 3 [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= - 3 \cdot \frac{1}{2}

Simplify

= - \frac{3}{2}

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