Find the two points of intersection

Question

Curve - y=x^2+1 Line - y=3x-1 Find the two points of intersection of the line and the curve. Calculate the area of the finite region bounded by the parabola and the line.

Answer 1

The curve is and the line is .

Substitute the value of in .

Factor by grouping.

Factor :

Apply zero product property.

.

Substitute the values  of in .

and .

Therefore, the two points of intersection of the line and curve are .

Area  .

.

Therefore, area of the finite region bounded by the parabola and the line is 5.5 square units.

Comments

Area of the finite region bounded by the parabola and the line is 0.16 square units.

Answer 2

The curve is and the line is .

Substitute the value of in .

Factor by grouping.

Factor :

Apply zero product property.

.

Substitute the values  of in .

and .

Therefore, the two points of intersection of the line and curve are .

Area  .

.

Therefore, area of the finite region bounded by the parabola and the line is 0.16 square units.