Does anyone know how to finish this problem?
#Help find integral
mossy monolith
serene brambleBOT
mossy monolith
I started the problem by adding 5 and -3 to 2 what do i do after? Shouldn't integral of a to -a be 2?
mossy monolith
@severe ice
proven python
Reading the problem, S[x] is odd, R[x] is even.
mossy monolith
Is this not how I start it?
Because it goes from -a to 0 then the other goes from 0 to a so wouldn’t I set it equal to integral of -a to a?
Given each area
severe ice
you have to have the same function in each integral tho
what you wrote here doesn't work at all
rich jasper
Yep, can do it that way, just take care of the odd/even functions and their symmetries
severe ice
$$\int_{-a}^{a} (2S(x) - R(x))\dd{x} = \int_{-a}^0 (2S(x) - R(x))\dd{x} + \int_{0}^a (2S(x) - R(x))\dd{x}$$
wary shardBOT
aPlatypus
severe ice
then you can split it further if you want
mossy monolith
and then i would substitue the given areas?
severe ice
yeah
mossy monolith
how would i get the variable a out of it? Is there an antiderivative I have to do
proven python
are you trying to solve the integrals without known functions for R[x] and S[x]?
severe ice
and use the oddness / evenness of R and S to get the areas that you don't know already
severe ice
you're misusing the rule
that's the problem
$$\int_a^b f(x) = \int_a^c f(x) + \int_c^b f(x)$$
wary shardBOT
aPlatypus
mossy monolith
where is the +3 from?
i never understood that part either
that was a reused study guide its not my writing
severe ice
where is the +3 from?
someone forgot to type it in the question lol
that's the only thing I can see
proven python
that's what I was wondering. No way I got any 'a' in my approaches without that +3.
mossy monolith
oh shoot nvm i remember my substitute saying something like that
lol
yeah the problem was mistyped
ty
proven python
you've got it from there?
mossy monolith
ill let yall know if i dont
but i get the process now
and i see where i was initially stuck on
proven python
Here's the symmetry the others were talking about earlier, just in case.
mossy monolith
**aPlatypus**
so since i missed the 3, would there also be a +3 in each integral now too?
severe ice
yea
mossy monolith
Here's the symmetry the others were talking about earlier, just in case.
i cant find the missing areas now
proven python
they give us two integrals, let's pick one and focus on that. Do you want to work on S[x] or R[x]?
mossy monolith
S(x)
proven python
we are given S[x] is odd and that the integral from 0 to a of S[x] is equal to -3
mossy monolith
yes
proven python
knowing S[x] is odd, this gives us a way to determine the integral of S[x] from -a to 0
mossy monolith
how is that
proven python
let's try an example. Let's take f[x] = x and integrate f[x] from 0 to 1
This is how the figure looks
mossy monolith
so would i draw it out and find the area from there?
proven python
that's one way to do it 🙂
proven python
If you know the area from x = 0 to x = 1, what do you think the area is from x = -1 to x = 0?
yes, exactly
They're giving you a value for S[x] integral for x = 0 to x = a. What do you think is the value of S[x] integral when we use x = -a to x = 0?
charred remnant
Why isn't this?
proven python
because the pink part was missing +3 in the integral
mossy monolith
so would -a to 0 of S(x) be positive 3?
proven python
yes
mossy monolith
@proven python for R(x) would it be double then?
proven python
very good
proven python
Here is an even function from x = -2 to x = +2
charred remnant
proven python
If we folded this across the y-axis (like closing a spiral notebook), the two sides would match up
charred remnant
finish it there guys
Since the integral from -a - 0 is even, it is equal to the integral from 0 to A
proven python
Here is a graph of another even function, this time from -pi to pi:
Just like Joaco indicates, the integral from -a to 0 of this function is the same number as integrating from 0 to a
If folding with imagination is difficult (usually is for me). You can sketch an even function on paper and fold that 🙂
mossy monolith
and just to clarify, for the 3 integral would it worklike an even function too sort of?
3a on both sides
proven python
yes
mossy monolith
ye thats what i drew
proven python
nice