What is the integral from 3 to 2 of 2x ?

The integral from 3 to 2 of 2x is -5

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integral from 3 to 2 of 2x

\int_{3}^{2} 2 x d x

- 5

Solution steps

\int_{3}^{2} 2 x d x

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

= - \int_{2}^{3} 2 x d x

Take the constant out:

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

= - 2 \cdot \int_{2}^{3} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{5}{2}

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

Simplify

= - 5

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{9} (x) d x

\int_{5}^{9} 1 d x

\int_{2}^{4} \frac{1}{x x - 1} d x

\int_{0}^{\frac{π}{4}} (cos^{2} (x)) d x

\int_{0}^{3} \frac{2}{3 x + 2} d x