Find the area bounded between the curve f(x) = 3x^2-4x +2 and the line y= 2x-1

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

First let us determine the points of intersection of the curve f(x) = 3x^2- 4x +2 and the line y= 2x-1.

2x - 1 = 3x^2 - 4x + 2

=> 3x^2 - 6x + 3 = 0

=> x^2 - 2x + 1 = 0

=> (x -1)^2 = 0

=> x = 1

The line is tangential to the curve.

There is no area bounded between the curve f(x) = 3x^2- 4x +2 and the line y= 2x-1.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

First we need to find the intersection points between the curve and the line.

==> f(x) = y

==> 3x^2 - 4x + 2 = 2x-1

==> 3x^2 - 6x + 3 = 0

==> We will divide by 3.

==> x^2 - 2x + 1 = 0

Now we will factor.

==> (x-1)^2 = 0

==> x = 1

There is only 1 intersection point between the curve and the line.  As a result there is no area bounded by the 2 equations.

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