Question

Sketch the graph of y = x |x| and hence find the area bounded by this curve, X-axis and the ordinates x = –2 and x = 2, using integration.

Answer 1

y = x lxl

y = x² if x>0 and

y = −x² if x<0

Required Area = `int_-2^2ydx`

`= int_-2^2 x |x| dx`

`=int_-2^0+x^2dx+int_0^2x^2dx`

`= + [x^3/3]_-2^0+[x^3/3]_0^2`

`= +[0-[(-2)^3/3]]+[2^3/3-0]`

`= +8/3+8/3 = 16/3 unit`