problem related to areas

Question

Find the area bounded by the curve y=x^2/4 + x/4 - 1/2 with x-axis in [0,2] 

Answer 1

y = (1/4)x²+(1/4)x-1/2 = f(x)

 

   = (1/4)[x²+x-2] = (1/4)(x+2)(x-1) = 0 when x = -2 or 1

 

When 0<x<1, y<0

When 1<x<2, y>0

 

Area = -∫_{(from 0 to 1)}f(x)dx + ∫_{(from 1 to 2)}f(x)dx

Answer 2

A = ∫_a^b f(x)dx

 

A = ∫₀² (x²/4 + x/4 - 1/2)dx

 

Can you finish from here?

Note: If you want only the area above the x-axis, first find the sub-intervals in [0,2] where f(x) is positive, and then integrate over those sub-intervals, and add up the results.