Sketch the graph and find the area of the region described below.

Question

f(x)= -3xe^((-x)^2)
Find the area of the region bounded below by the graph of f(x) and above by the x-axis from x = 0 to x = 3.

Answer 1

Did you mean it as typed? because (-x)^2 is the same as (x^2) I get the feeling you meant

∫[0,3] 0-(-3xe^(-x^2)) dx
Let u = x^2 so
du = -2x dx and you have

∫[0,9] -3/2 e^-u du

Now it's a cinch, eh?