Integral problem?

Question

e^-(x^2) from 1 to 2

I tried that substituiton doesnt work

So it is not possible to solve.... =/

Answer 1

Sorry, the integral of "e raised to the minus x squared power" with constant limits is impossible. Normally, you find the antiderivative and go from there. But mathematicians have determined that this particular function has no elementary antiderivative. Unless you are in a *very* advanced calculus class, evaluating this is impossible. :-/

The reason u-sub doesn't work is because when you substitute u for x^2, you get that extra 2x, but that 2x has nothing to cancel out with. You are stuck with int 1/(2x)*e^(-u) du, but you can't go on with the integration because you have both x and u, and that's illegal in the world of mathematics.

Answer 2

Use a graphing calculator that can calculate the value of definite integrals. We entered e^(-x^2) into the function list of a TI - 83 Plus and produced a graph of the function. Under the calculators CALC menu is the option INT f(x) dx. (We use INT in place of the integral symbol.) When that option is chosen, the calculator asks for the lower and upper limits of integration. The calculator then shows the area between the function and the x-axis from x = 1 and x = 2. The approximate value of the area 0.1353 square units.

Answer 3

No, substitution won't do you much good.
If you let u = x² then x = √u, dx = du/(2√u), you get an integral.
which is just as hard to evaluate.
In fact, your integral has no elementary antiderivative
and its solution involves the error function.

Answer 4

e^(u)

= 1/u*e^(u+1) + C

= 1/(x^2) * e^(x^2+1) + C

That should get you started

Answer 5

I would suggest using u-substitution on this one, with u=x^2. From there, you should hopefully be able to get it.