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Popular Calculus >

integral from 3 to 1 of (-5x+9)

Solution

\int_{3}^{1} (- 5 x + 9) d x

Solution

2

Solution steps

\int_{3}^{1} - 5 x + 9 d x

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

= - \int_{1}^{3} - 5 x + 9 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}^{3} 5 x d x + \int_{1}^{3} 9 d x)

\int_{1}^{3} 5 x d x = 20

\int_{1}^{3} 9 d x = 18

= - (- 20 + 18)

Simplify

= 2

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 3 to 1 of (-5x+9) ?
The integral from 3 to 1 of (-5x+9) is 2