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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

enter image description here

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.

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

enter image description here

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

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  • $\begingroup$ Brother what app do you use specifically to sketch these graphs? $\endgroup$ – Zlatan Sep 1 '16 at 0:39
  • $\begingroup$ @Zlatan Desmos online calculator. It's great. Hear's the graph: desmos.com/calculator/egwlyidxma $\endgroup$ – Carser Sep 1 '16 at 0:40
  • $\begingroup$ 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. $\endgroup$ – Zlatan Sep 1 '16 at 0:43
  • $\begingroup$ @Carser +1 and next +1 in mind for the calculator. :-) $\endgroup$ – Przemysław Scherwentke Sep 1 '16 at 0:43
  • $\begingroup$ Just an obvious question, do you think this question deserves an upvote? $\endgroup$ – Zlatan Sep 1 '16 at 0:44
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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.)

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  • $\begingroup$ Hey thanks for the help and can you offer me any advice about closing down a question? $\endgroup$ – Zlatan Sep 1 '16 at 0:47
  • $\begingroup$ @Zlatan I would suggest not to close your question. Carser's answer may be useful for future users. $\endgroup$ – Przemysław Scherwentke Sep 1 '16 at 0:50
  • $\begingroup$ Okay I won't close the question but still if I wanted to then how could I possibly do it? $\endgroup$ – Zlatan Sep 1 '16 at 0:54
  • $\begingroup$ @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. $\endgroup$ – Przemysław Scherwentke Sep 1 '16 at 1:03

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