# Area between curves using integrals

Okay so I have to find the area bounded by $y= x^2-3x+2,x=1,x=2$ and $y=0$

I sketched the graphs and tried to solved it like this

Okay so I took the integral for the quadratic from $x=1$ to $x=2$ which should give me the area of the curved part (which is the required answer) plus all the area above x axis and in between $x=1$ to $x=2$. I know I need to subtract this second area but don't know how. Any help would be appreciated.

• It's hard to tell sideways, but it looks like you forgot to divide by $3$ in the first anti-derivative. – Carser Sep 1 '16 at 0:34
• Yes rightly said I saw it now. Stupid mistake. And thank you all friends. – Zlatan Sep 1 '16 at 0:36

Just inspecting it,

it seems like this simplifies to $$\left| \int_{1}^{2}x^2-3x+2 \ dx \right|$$ $$= \left| \left[ \frac{1}{3}x^3 -\frac{3}{2}x^2+2x \right]_{1}^{2} \right|$$ $$= \left| \left( \frac{(2)^3}{3}-\frac{3(2)^2}{2}+2(2)\right)-\left(\frac{(1)^3}{3}-\frac{3(1)^2}{2}+2(1)\right) \right|$$

• Brother what app do you use specifically to sketch these graphs? – Zlatan Sep 1 '16 at 0:39
• @Zlatan Desmos online calculator. It's great. Hear's the graph: desmos.com/calculator/egwlyidxma – Carser Sep 1 '16 at 0:40
• Alright. Lol bro you're just solving the whole integral step by step. That's great but I already got the answer I was looking for. – Zlatan Sep 1 '16 at 0:43
• @Carser +1 and next +1 in mind for the calculator. :-) – Przemysław Scherwentke Sep 1 '16 at 0:43
• Just an obvious question, do you think this question deserves an upvote? – Zlatan Sep 1 '16 at 0:44

HINT: Area=$\int_{a}^{b} (u(x)-l(x))\,dx$, where $u$ is the upper and $l$ is the lower function. In your case $u(x)=0$ on $[1,2]$.

(Rotating of your picture is probably an easy method to see limits of interval and the limiting functions.)

• Hey thanks for the help and can you offer me any advice about closing down a question? – Zlatan Sep 1 '16 at 0:47
• @Zlatan I would suggest not to close your question. Carser's answer may be useful for future users. – Przemysław Scherwentke Sep 1 '16 at 0:50
• Okay I won't close the question but still if I wanted to then how could I possibly do it? – Zlatan Sep 1 '16 at 0:54
• @Zlatan You are probably thinking not about closing (making inactive) but deleting your question. You have gray delete under your question. I am not sure if always or some level of reputation is needed. – Przemysław Scherwentke Sep 1 '16 at 1:03