If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Warmup: Definite integral properties (no graph)

Apply the properties of definite integrals to evaluate definite integrals.

## Problem 1

Given ${\int }_{-5}^{-1}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=4$, ${\int }_{3}^{5}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=9$, and ${\int }_{-5}^{5}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=10$, find the following:
a) ${\int }_{-1}^{3}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

b) ${\int }_{-1}^{5}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

c) ${\int }_{-5}^{-1}7f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

d) ${\int }_{5}^{-5}f\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

### Challenge

e*) ${\int }_{3}^{5}\left(f\left(x\right)+4\phantom{\rule{0.167em}{0ex}}\right)dx=$

## Problem 2

Given ${\int }_{-8}^{-2}g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=11$, ${\int }_{-8}^{0}g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=5$, and ${\int }_{-2}^{8}g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=-5$, find the following:
a) ${\int }_{-2}^{0}g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

b) ${\int }_{0}^{8}g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

c) ${\int }_{8}^{-8}10g\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=$

### Challenge

d*) ${\int }_{0}^{8}\left(g\left(x\right)+x\right)dx=$

## Want to join the conversation?

• In the final challenge question, how do we know to use the graph of y = x?