What is the integral from 1 to 2 of 4x ?

The integral from 1 to 2 of 4x is 6

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integral from 1 to 2 of 4x

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

6

Solution steps

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

Take the constant out:

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

= 4 \cdot \int_{1}^{2} x d x

Apply the Power Rule

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

= 4 [\frac{x ^{2}}{2}]_{1}^{2}

Compute the boundaries:

\frac{3}{2}

= 4 \cdot \frac{3}{2}

Simplify

= 6

\int_{0}^{1} x^{2} (1 - x) d x

\int_{0}^{1} e^{- s t} t^{2} d t

\int_{- 2}^{4} (2 x - \frac{x ^{2}}{2}) d x

\int_{- 1}^{2} (1 - t^{2}) t d t

\int_{0}^{y} y d y