Question

homework 1: 1.1-1.4 review
score: 7/17 answered: 4/13
question 5
given that \\(\int_{2}^{9} f(x) dx = \frac{38}{11}\\), what is \\(\int_{9}^{2} f(r) dr\\)?
\\(\int_{9}^{2} f(r) dr = \\)
question help: video

Explanation:

Step1: Recall reverse interval property

For any integrable function $f$, $\int_{a}^{b} f(x) dx = -\int_{b}^{a} f(x) dx$.

Step2: Apply property to given integral

We know $\int_{2}^{9} f(x) dx = \frac{38}{11}$, and the variable name (x vs r) does not affect the value of the definite integral. So:
$\int_{9}^{2} f(r) dr = -\int_{2}^{9} f(r) dr = -\frac{38}{11}$

Answer:

$-\frac{38}{11}$