Question

Determine whether the integral is convergent or divergent.

∞	13xe-x^2 dx
−∞

convergentdivergent

If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)

Answer 1

Determine whether the integral 13xedt is convergent or divergent. The graph of the function f(x)-13xer Is shown below 10 6 5 4 2 5 -4.54 -3.5 -3-2.5 -2-1.5-1-0.50.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 This integral is improper both because the upper limit is oo and the lower limit is -o. Break the integral into two parts at, say x 0

Evaluate the two integrals separately 13 when x-> 0, then t → 0 13 13 1+ lim e 13 13 -1+e 13 [-1 +0] [Since e":0] 13

Therefore, 13 13 Hence, the original integral 13xdx converges to 0