how do I change the limits? I thought I was suppose to 2 and 1 for $$\theta$$
$$\int_{1}^{2} \frac{\sqrt(x^2 -1)}{x}dx$$
$$x = sec\theta$$
$$dx = tan\theta \sec \theta d\theta$$

Question

how do I change the limits? I thought I was suppose to 2 and 1 for $$\theta$$
$$\int_{1}^{2} \frac{\sqrt(x^2 -1)}{x}dx$$
$$x = sec\theta$$
$$dx = tan\theta \sec \theta d\theta$$

anonymous · Answer

$$=\int tan^2 \theta d\theta$$

anonymous · Answer

$$\int \frac{\sqrt(sec^2 \theta -1)}{sec\theta}* tan\theta sec\theta d
\theta$$
$$\int \frac{tan\theta}{sec\theta}* tan\theta sec\theta d
\theta$$

anonymous · Answer

i forgot how to change the limit....thought I had to plug in 2 and 1 for theta ...but that's wrong

turingtest · Answer

$$2=\sec\theta=\frac1{\cos\theta}\implies\cos\theta=\frac12\implies\theta=\frac\pi3$$$$1=\sec\theta\implies\cos\theta=1\implies\theta=0$$

turingtest · Answer

we are just putting the numbers in and finding out what theta is based on our substitution

anonymous · Answer

life saver! thanks!

turingtest · Answer

welcome :)

anonymous · Answer

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