Question

If f′(x)=x(e)^(x^2) and f(0)=6, then
f(x)=?

Answer 1

Integrate f'(x). \[\int\limits_{}^{} x(e^{x^{2}})dx \] to get f(x).

To do that, you do the "suck up" rule: u = x^2, du/2=xdx.
\[1/2\int\limits_{}^{}e^{u}du\]

Integral of e^u is e^u, so you would end up getting: 1/2(e^x^2) + C = f(x) (remember, u = x^2)

Since you're given f(0) = 6, plug that into the f(x) equation you go to calculate the value of C. The final answer should be: 1/2(e^x^2) + 5.5