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

The integral from 2 to 3 of (3-x)/2 is 1/4

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

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

\frac{1}{4}

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2}^{3} 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

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

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

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

= \frac{1}{2} (3 - \frac{5}{2})

Simplify

\frac{1}{2} (3 - \frac{5}{2}) : \frac{1}{4}

= \frac{1}{4}

\int_{1}^{5} \frac{4}{x} - \frac{4}{x ^{2}} d x

\int_{4}^{8} x^{2} d x

\int_{a}^{x} \frac{f ( t )}{t ^{2}} d t

\int_{0}^{3} arctan (x) d x

\int_{0}^{4} \frac{1}{( 4 - x ) ^{\frac{3}{2}}} d x

What is the integral from 2 to 3 of (3-x)/2 ?
The integral from 2 to 3 of (3-x)/2 is 1/4