# Definite intergration area under curve bounded with line

• thomas49th

## Homework Statement

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

## 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 don't 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 :)

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.

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

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. ahhh i see cheerz :)