Find area contained by the curve

[andrey21]

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

Homework Equations

I don't 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 ??

 

[Mark44]

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

Homework Equations

I don't 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 ??

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.

 

[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

 

[Mark44]

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))$\Delta x$.

 

[andrey21]

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

 

[Mark44]

Yes.