What is the integral from 1 to 3/2 of (2-x-1/3 x) ?

The integral from 1 to 3/2 of (2-x-1/3 x) is 1/6

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integral from 1 to 3/2 of (2-x-1/3 x)

\int_{1}^{\frac{3}{2}} (2 - x - \frac{1}{3} x) d x

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\int_{1}^{\frac{3}{2}} 2 - x - \frac{1}{3} x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{\frac{3}{2}} 2 d x - \int_{1}^{\frac{3}{2}} x d x - \int_{1}^{\frac{3}{2}} \frac{1}{3} x d x

\int_{1}^{\frac{3}{2}} 2 d x = 1

\int_{1}^{\frac{3}{2}} x d x = \frac{5}{8}

\int_{1}^{\frac{3}{2}} \frac{1}{3} x d x = \frac{5}{24}

= 1 - \frac{5}{8} - \frac{5}{24}

Simplify

1 - \frac{5}{8} - \frac{5}{24} : \frac{1}{6}

= \frac{1}{6}

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What is the integral from 1 to 3/2 of (2-x-1/3 x) ?
The integral from 1 to 3/2 of (2-x-1/3 x) is 1/6