Definite intergration area under curve bounded with lineby thomas49th Tags: bounded, curve, definite, intergration, line 

#1
May2508, 01:31 PM

P: 656

1. The problem statement, all variables and given/known data
A cruve has the equation [tex]y = x{3}  8x^{2} + 20x [/tex]. The curve has stationary points A and B. There is a line through B parallel to y axis and meets the x axis at the point N. The region R is bounded by the curve , the xaxis and the line from A to N. Find the exact area under the curve 2. Relevant equations 3. The attempt at a solution Well I found the x coords of A and B, which is [tex]\frac{10}{3}[/tex] or 2. I intergrated the curve and got [tex]\frac{4x^{3}}{4}  \frac{8x^{3}}{3}+10x^{2}[/tex] no +C as we'll be having limits i presume But i dont know how to get the area of region R... as there is a stupid line in the way!!! Can somebody show/help me to do it. Thanks :) 



#2
May2508, 02:11 PM

P: 64

Hey
My first advice is to a picture of your problem. After that you notice that the exercise is to calculate the integral from x=A to x=B of f, i.e. integration of a polynomial. I expect you know how to do that. 



#3
May2508, 03:51 PM

P: 656

i can intergrate a polynominal easily and in the question paper there is a picture of the question. But because of this AN line, it's thrown me. How would you go about doing it.
Thanks 



#4
May2508, 07:07 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

Definite intergration area under curve bounded with line
Hi thomas!
If I've understood the question right, all you have to do is add a triangle (whose area is obvious), and you get the standard integral. 



#5
May2608, 07:37 AM

P: 656

ahhh i see cheerz :)



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