Homework SourseLet fx o if x is less than 0 x if 0 is less than or equal t
Let f(x) =
o if x is less than 0
x if 0 is less than or equal to x which is less than or equal to 1
2-x if 1 is less than x which is less than or equal to 2
0 if x is greater than 2
find g(x) = integral from 0 to x f(t) dt
I need the 3rd expression. I cant seem to figureit out but i have the first 2 and the 4th,
which are 0, (x^(2))/2 and 1 respectively.
Also where is f and g differentiable at? Use interval notation.
o if x is less than 0
x if 0 is less than or equal to x which is less than or equal to 1
2-x if 1 is less than x which is less than or equal to 2
0 if x is greater than 2
find g(x) = integral from 0 to x f(t) dt
I need the 3rd expression. I cant seem to figureit out but i have the first 2 and the 4th,
which are 0, (x^(2))/2 and 1 respectively.
Also where is f and g differentiable at? Use interval notation.
Solution
g(x) = integral of xf(t) g(x) = integral of x*x (from 0 to 1) + integral of x(2-x) (from 1 to 2) g(x) = integral of x^2 (from 0 to 1) + integral of (2x-x^2) (from 1 to 2) g(x) = x^3/3 [limit from 0 to 1] + x^2 - x^3/3 [limit from 1 to 2] apply limits g(x) = 1/3 + [4 - 8/3 - 1 + 1/3] g(x) = 1 g(x) is not differentiable at x = 1 because g\'(x) at x = 1- is equal to 1 & at x = 1+ is equal to -1
