# Math Help - Evaluating trig function

1. ## Evaluating trig function

My original integral has the following limits $\int_2^4$ and l use the following substitution $x=2sec\theta$. My question is how do l change the limits of the integral ?

Attempt to solution:

$x=2sec(2)$

x=2cos1\2

Is this correct ?

2. Hello, nyasha!

My original integral has the following limits $\int_2^4$
. . . . . . and l use the following substitution: $x\:=\:2\sec\theta$.

My question is: How do l change the limits of the integral ?

Note that the limits are for ${\color{blue}x}\!:\;\;\int^{x=4}_{x=2}f(x)\,dx$

For the upper limit, $x = 4$, we have:. $4 \:=\:2\sec\theta \quad\Rightarrow\quad \sec\theta \:=\:2\quad\Rightarrow\quad \theta \:=\:\frac{\pi}{3}$

For the lower limit, $x = 2$, we have: . $2 \:=\:2\sec\theta \quad\Rightarrow\quad \sec\theta \:=\:1 \quad\Rightarrow\quad \theta \:=\:0$

So your integral becomes: . $\int^{\frac{\pi}{3}}_0 g(\theta)\,d\theta$