Question

Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

Answer 1

The lines are y = 3x^2, y = 6x - 3, and y = 0

Answer 2

do i have to integrate the area from 0-1 as well

Answer 3

also the tangent line is 6x - 3

Answer 4

Alright i figured it out, so basically the representation is
\[\int\limits_{0}^{1/2} 3x^2 + \int\limits_{1/2}^{1} (3x^2 - (6x - 3))\]

Answer 5

= 1/4

Answer 6

Thanks anyway!

Answer 7

@sami-21 , y=6x-3 was the equation of tangent line
so, the area is :
A = int [0,3] (3x^2) dx