For the following three (03) items: Consider the function f(x) = x|x| . What is the area bounded by the curve f(x) , the x -axis and the lines x = -2 and x = 1 ?

Step-by-step solution

The given function is f(x) = x|x| . The required area bounded by the curve f(x) , the x -axis and the lines x = -2 and x = 1 is given by: A = _ -2 ¹ |f(x)| dx A = _ -2 ¹ |x|x|| dx Since |x|x|| = |x|^2 = x^2 , we have: A = _ -2 ¹ x^2 dx A = [ x^3 3 ]_ -2 ¹ A = 1^3 3 - (-2)^3 3 A = 1 3 - ( - 8 3 ) A = 9 3 = 3 Answer: 3