I have no idea what I am doing wrong. I keep getting one when I should be getting two. It is part of a numerical integration problem. I've got the numerical integration part down which is ironic. The part I am having problems with is finding the actual value of the integral. I need this to find the error of the trapezoid and Simpson's estimations.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The integral is:

[tex]\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{3\cos(t)dt}{\left(2+\sin(t)\right)^{2}} = 2[/tex]

I know it equals 2 cause of the integrate function on my calculator. I am trying to figure out where I am going wrong with my algebra.

2. Relevant equations

[tex]\int^{a}_{-a} x dx = 2\cdot\int^{a}_{0} x dx[/tex]

[tex]Let u = sin(t) + 2, du = cos(t)dt[/tex]

3. The attempt at a solution

So we start by saying:

[tex]\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{3\cos(t)dt}{\left(2+\sin(t)\right)^{2}} [/tex]

We can use the above property of integration to change this to:

[tex]2\cdot\int^{\frac{\pi}{2}}_{0} \frac{3\cos(t)dt}{\left(2+\sin(t)\right)^{2}} [/tex]

We then use u substitution thus we can say:

[tex]x=0 \rightarrow u=2[/tex]

[tex]x= \frac{\pi}{2} \rightarrow u=3[/tex]

so we get:

[tex]2\cdot\int^{3}_{2} \frac{3du}{u^{2}} [/tex]

We can shove the 3 out front and then integrate the resulting [tex]\frac{du}{u^{2}}[/tex]

Thus we get:

[tex]6\cdot\frac{-1}{u}[/tex] Evaluated from 2 to 3.

This goes to:

[tex]6\cdot\left(\frac{-1}{3}-\frac{-1}{2}\right)[/tex]

Which in turn goes to:

[tex]6\cdot\frac{1}{6} = 1[/tex]

I don't know what I am doing wrong. Please help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration problem

**Physics Forums | Science Articles, Homework Help, Discussion**