To find the are bounded by the curve
F(x) = xe^(x^2) and the limits a=-2 and b=-1
So I integrate the function using substitution
$\displaystyle u=x$ and get stuck on how to go on
Help much appreciated!! thanks!!!
To find the are bounded by the curve
F(x) = xe^(x^2) and the limits a=-2 and b=-1
So I integrate the function using substitution
$\displaystyle u=x$ and get stuck on how to go on
Help much appreciated!! thanks!!!
I think you are on the wrong track. Look at the function:
$\displaystyle xe^{x^2}$
Now integrate it simply, don't use any U-Substitution.
$\displaystyle \int{xe^{x^2}}dx = \frac{1}{2}e^{x^2} + C$
I'll let you take it from there. If you still don't know how to do it, feel free to ask me.
The formula for the volume of any function rotated around $\displaystyle y=k$ is given by $\displaystyle V=\int_a^b \pi (R^2 - r^2) dx$ where a and b are the limits of integration, R (outer radius) is the distance from the axis of rotation to the further side of the elemental strip and r (inner radius) is the distance from the axis of rotation to the closer side of the elemental strip. In your case, since the axis of rotation is the x-axis, which is $\displaystyle y=0$, your r is simply 0. This will cancel out and your formula will become $\displaystyle V=\int_a^b \pi R^2 dx$.
Your R (outer radius) is simply the function because your axis of rotation is the x-axis.
Your answer becomes:
$\displaystyle V=\int_1^2 \pi (f(x))^2 dx$
Hope I helped
Do you get it now?
Oh you wrote the function weirdly before with LaTex and I wasn't sure what you meant.
$\displaystyle \int_1^2 \pi e^x \sqrt{x} dx$
Well, this is actually a non-elementary integral. This is impossible to compute normally. If you are more advanced in calculus you can do it, though. Do you know Dawson's function?
Well the answer to the indefinite integral is $\displaystyle e^x(\sqrt{x}-F(\sqrt{x}) + C$ where F is the Dawson Function. Yeah, a first (or even second) year calc student would not be responsible for being able to do this integral. Are you sure you weren't allowed to use a graphing calculator?