Question

Sketch the graph (Do this on paper. Your teacher may ask you to turn in this graph.) and find the area of the region bounded below by the graph of the function and above by the x axis from x = 0 to x = 1.
f(x) = -xe^(-x^2) x=0 x=1

Answer 1

∫[0,1] -x e^(-x^2) dx
let u = -x^2, and you have du = -2x dx,
∫[0,-1] (1/2) e^u du
= (1-e)/(2e)