Question

Find the area of the region bounded by y=x^3-3x^2+2x and the x-axis.

Answer 1

sketch the graph first.

= integral from 0 to 1 of (x^3 - 3x^2 + 2x) + |integral from 2 to 1 of (x^3 - 3x^2 + 2x)|

= [x^4/4 - x^3 + x^2]1,0 + |[x^4/4 - x^3 + x^2]2,1|

= 1/4 - 1 + 1 + |4 - 8 + 4 - (1/4 - 1 + 1)|

= 1/4 + |-(1/4)|

= 1/4 + 1/4 = 1/2