Question

exercises 1.2 the definite integral
score: 120/170 answered: 12/17
question 13
given that \\(\int_{4}^{6} f(x) dx = \frac{8}{3}\\), what is \\(\int_{6}^{4} f(r) dr\\)?
answer =
question help: video message instructor
submit question jump to answer

Explanation:

Step1: Recall reverse interval property

For any definite integral, $\int_{a}^{b} f(x)dx = -\int_{b}^{a} f(x)dx$. Also, the variable of integration is a dummy variable, so $\int_{4}^{6} f(x)dx = \int_{4}^{6} f(r)dr$.

Step2: Apply property to the given integral

We know $\int_{4}^{6} f(x)dx = \frac{8}{3}$, so $\int_{6}^{4} f(r)dr = -\int_{4}^{6} f(r)dr = -\frac{8}{3}$.

Answer:

$-\frac{8}{3}$