Finding area between two curves

Question

y=3-x^2 , y=2x, x=0, x=2

Answer 1

y = 3 - x²    is the upper curve

y = 2x   is the lower curve.

 

First, we want to see if these two curve intersect in between the bounds.

 

3 - x² = 2x

 

0 = x² + 2x - 3

 

0 = (x + 3)(x - 1)

 

       x = -3    or    x = 1

 

But since x=1 is with the bounds, we use this as our reference.

 

When you graph the curves in the bounds, there will be two areas covered by the bounds.  You need to add up those areas.

 

 

Area =

  ¹∫₀ (3 - x²)dx  -  ¹∫₀ (2x)dx + ²∫₁ (2x)dx  -  ²∫₁ (3 - x²)dx