Find the area of the region bounded by the parabola y = 2x^2, the tangent line to this parabola at (4, 32), and the x-axis.

Attempt:
(please see attachment)

Question

Find the area of the region bounded by the parabola y = 2x^2, the tangent line to this parabola at (4, 32), and the x-axis.

Attempt: 
(please see attachment)

anonymous · Answer

attachment

anonymous · Answer

are not the boundaries x = 0 and x = 4?

turingtest · Answer

I think the equation of your line is wrong

turingtest · Answer

maybe not... sorry

anonymous · Answer

I checked twice. You take the derivatie and you get 4x. You plug in x = 4 and you get slope 16

anonymous · Answer

brb

turingtest · Answer

oh I thin I see your problem: you want the area above the x axis only, so you need 2 integrals

turingtest · Answer

one from x=0 to where the line intersects the x-axis (for which the lower bound will be just x=0), and one from that point to x=4 (for which the lower bound will be the line)

anonymous · Answer

Why can I not just do from x =1 to x = 4?

turingtest · Answer

|dw:1337111172971:dw|I do believe the line hits the x-axis at x=2, no?

turingtest · Answer

|dw:1337111251878:dw|zoom in