# Definite intergration area under curve bounded with line

by thomas49th
Tags: bounded, curve, definite, intergration, line
 P: 656 1. The problem statement, all variables and given/known data A cruve has the equation $$y = x{3} - 8x^{2} + 20x$$. 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 x-axis 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 co-ords of A and B, which is $$\frac{10}{3}$$ or 2. I intergrated the curve and got $$\frac{4x^{3}}{4} - \frac{8x^{3}}{3}+10x^{2}$$ 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 :)
 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.
 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
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.
 P: 656 ahhh i see cheerz :)

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