$$Sketch~the~graph~of~~~y=xe^{-x^2} ~~~for~~~~x0.$$$$ ~Find~the~area~contained~\between~this~graph~and~the~positive~x-axis$$

Question

$$Sketch~the~graph~of~~~y=xe^{-x^2} ~~~for~~~~x>0.$$$$ ~Find~the~area~contained~\between~this~graph~and~the~positive~x-axis$$

anonymous · Answer

Hey, tiaph, I'm going. I'll see the post when you write it! :)

anonymous · Answer

I tried sketching the graph out for u but i couldnt, so here is a link, http://www.wolframalpha.com/input/?i=x*e^%28-x^2%29 since the question asks for the graph for x>0 take note to draw only that part of the graph u see in the link. To find the area, u neecd to integrate the function. $$\int\limits_{0}^{\infty}x \times e ^{-x ^{2}} $$ Integrating it, u get. $$-\frac{1}{2 e ^{x ^{2}}}+c $$, where c is a arbitrary constant. Proceed to solve the definite integrals. $$- \frac{1}{2e ^{\infty ^{2}}} -( - \frac{1}{2e ^{0^{2}}}) = 0 + \frac{1}{2} =\frac{1}{2}$$ e^ infinity is infinity. 1divided by infinity can be approximated to be 0.

anonymous · Answer

Hm... Ok thanks!!! :)

anonymous · Answer

Np!