# A2 Integration Question

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#1
Can someone explain how i should integrate this:
.
The way that I tried gives:
which, when I insert the values to get:
-
I end up with my calculator telling me there's an error.
I'm guessing this error is because: isn't possible.
Can someone explain where/if i'm going wrong and how I should approach this?

Thanks.
0
6 years ago
#2
the problem is that the underneath will reach zero somewhere between the limits 2 and 3
1
6 years ago
#3
Because the denominator is infinite between llimits, as thebear indicated, you have to use "improper integrals" and limits. Try expressing the integrand as:

using partial fractions, you can then have 3 integrals - the 2nd 2 improper - the first one having limits between 2 and 3, the 2nd between 2 and root(5)-a small arbitrary number, epsilon, and 3rd one having limits between root(5)+a small arbitrary number epsilon.

then, evaluate the first by taking:

and the 2nd one as:

(admiteddly, evaluating the integrand without limits similar to the way you have is easier, then taking limits as i have at the points of infinity is speedier)
0
6 years ago
#4
Plot F(x) into your GC and get the graph. You will see that x=5^1/2 is a vertical asymptote as y tends to infinity
0
6 years ago
#5
(Original post by fincle1)
Can someone explain how i should integrate this:
.
The way that I tried gives:
which, when I insert the values to get:
-
I end up with my calculator telling me there's an error.
I'm guessing this error is because: isn't possible.
Can someone explain where/if i'm going wrong and how I should approach this?

Thanks.

When we integrate a function that leads to ln gives ln|f(x)| so
0
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