Find area contained by the curve

1. May 10, 2010

andrey21

FInd the area contained by the curve and the x axis
y = (2x-7)(x+4)

2. Relevant equations

I dont know really where to start all I have done is multiply out the brackets like so
y = 2x^(2) + x - 28

Will the curve cross the x axis at x = -4 and x = 7/2 ??

2. May 10, 2010

Staff: Mentor

Yes, of course. Since you are supposed to find the area between this curve and the x axis, you will need to set up a definite integral.

3. May 10, 2010

andrey21

Ok so i set up the definite integral:

Next I integrated the equation to give me:

2/3 x^(3) +x^(2)/2 -28x

I then subst in values and gave me a final value of:
-140 5/8

Is this correct? Sorry bad formatting on integration

4. May 10, 2010

Staff: Mentor

For what you did, that answer is correct, but what you did isn't correct. The area should never be negative. The region whose area you are finding lies beneath the x-axis, so the area of your typical area element is (0 - (2x2 + x - 28))$\Delta x$.

5. May 10, 2010

andrey21

Ah I see but it will just come out with the same answer but positive if I adopt the method u suggest?

6. May 10, 2010

Yes.