Let .
Find
and
How can I go about solving this? I've done examples on definite integrals and did my note-reading but nowhere does it explain how to deal with this kind of problem. Any help is appreciated!
properties of definite integrals you should already be familiar with ...
$\displaystyle \int_a^b f(x) \pm g(x) \, dx = \int_a^b f(x) \, dx \pm \int_a^b g(x) \, dx$
$\displaystyle \int_a^b k \cdot f(x) \, dx = k \int_a^b f(x) \, dx$
$\displaystyle \int_a^b f(x) \, dx = -\int_b^a f(x) \, dx$
$\displaystyle \int_a^b f(x) \, dx + \int_b^c f(x) \, dx + \int_c^d f(x) \, dx = \int_a^d f(x) \, dx$
Thank you! I got the first one.
For the second, I notice that the upper limit is actually a smaller value than the lower. So that means I can flip them and make the integral negative? Even so, the 6f(x)-10 throws me off... Do I replace the f(x) with -10 (which was the answer to the previous question) and solve?
$\displaystyle 6 \int_8^{5.5} f(x) \, dx - \int_8^{5.5} 10 \, dx = -6
\int_{5.5}^8 f(x) \, dx + \int_{5.5}^8 10 \, dx
$
Since $\displaystyle -6 \int_{5.5}^8 f(x)$ = -10, the equation becomes
$\displaystyle -6 * -10 + \int_{5.5}^8 10 \, dx$
What can I do to the second one to change that into a number too?