Question

Calculus I Question (Semi-Challenging):

Answer 1

Find: \(\large \int_{-2}^{3}2x^2[~|x|~]dx\)

Answer 2

Do those brackets (not the absolute value signs) denote anything? Like the floor or ceiling function? or are they being used like parenthesis?

Answer 3

Largest integer \(\leq\) x
sorry about that

Answer 4

So its the floor function then. Your best bet is the break the integral up into segements whos length is 1:\[\int\limits_{-2}^{3}\mbox{JUNK}\]\[=\int\limits_{-2}^{-1}\mbox{JUNK}+\int\limits_{-1}^{0}\mbox{JUNK}+\int\limits_{0}^{1}\mbox{JUNK}\]\[+\int\limits_{1}^{2}\mbox{JUNK}+\int\limits_{2}^{3}\mbox{JUNK}\]

Answer 5

actually, this wasnt challenging as I thought. Lol. i guess just tedious work. Lol :/ guess i need to find another question for you, @joemath314159

Answer 6

You'll want to evaluate them separately. For example:\[\int\limits_{-2}^{-1}2x^2[|x|]dx.\] On the interval [-2,-1], |x|=-x, so we get:\[\int\limits_{-2}^{-1}2x^2[-x]dx.\]If x is in [-2,-1], then -x is in [1,2], and it follows that [-x]=1 so we get:\[\int\limits_{-2}^{-1}2x^2dx\]which is easy to evaluate.

Answer 7

yeah it is a bit tediuous >.<