# Math Help - Simple integration problem

1. ## Simple integration problem

When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.

Thanks for the help.

2. $4\sin^2t+4\cos^2t=4(\sin^2t+\cos^2t)=4$

So you need to compute

$\int\sqrt{29}\,dt$

Does that make sense?

3. Originally Posted by Undefdisfigure
When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.

Thanks for the help.
Maybe it is simply that you aren't familiar with typing these, but
cos^2(t) = cos(t)^2 = $cos^2(t) = cos(t) \times cos(t)$

cos(t^2) = $cos(t^2)$

-Dan

4. Originally Posted by Undefdisfigure
When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.

Thanks for the help.
Use the identity: $cos^2x + sin^2x = 1$
Therefore:

$
\int \sqrt{4cos^2x + 4sin^2x +25}\,dx = \int \sqrt{4(cos^2x + sin^2x) +25}\,dx = \int \sqrt{4 +25}\,dx
$

$
\int \sqrt{29}\,dx = \sqrt{29}x + C\
$