# Area between a function and its tangent

1. Sep 22, 2008

### Momentum09

1. The problem statement, all variables and given/known data
Find the area of the region bounded by the graph of f(x) = 4x^2, the tangent line to this graph at P(2, f(2)), and the x-axis

2. Relevant equations

Integral of [f(x)-g(x) dx]

3. The attempt at a solution
I first tried to find the equation for the tangent line
The derivative of 4x^2 = 8x, subsituting x=2 into the equation I got 16 [slope]
the equation then turned out to be y-2 = 16 (x-2) --> y = 16x-30
I then subtracted this tangent equation from 4x^2 then integrate, but I wasn't able to get the right answer.
Please show me how...thank you!

2. Sep 22, 2008

### CompuChip

Why did you have y - 2 = 16(x - 2)? If I plug in x = 2 I think it is not a tangent line...

3. Sep 22, 2008

### tiny-tim

Hi Momentum09!

I'll just add to what CompuChip says …

why not just integrate under the parabola in the usual way, and then subtract the area of the triangle using half-base-times-height?