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

Homework Equations

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 :)

 

[eys_physics]

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.

 

[thomas49th]

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

 

[tiny-tim]

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.

 

[thomas49th]

ahhh i see cheerz :)