Question

Bit stuck here

posting question..

Answer 1

\(\int_{0}^{\frac{\pi}{2}}\sec^{2}\left(\frac{x}{k}\right)dx=k \) Find k where \( 0\le k \le\pi\)

Answer 2

\( u=\frac{x}{k} \) \(\frac{du}{dx}=\frac{1}{k}\) \(kdu=dx\) \(\int_{0}^{\frac{\pi}{2}}\sec^{2}\left(u\right)k\ du = k\) \(\left[k\tan\left(\frac{x}{k}\right)\right]_{0}^{\frac{\pi}{2}}=k\) \(\frac{\pi}{2}\tan\left(\frac{\frac{\pi}{2}}{k}\right)-0=k\)

Answer 3

That was my work ^
I am stuck because it seems like it won't work. Tan is undefined at pi/2. I think my methodology is wrong, can someone tell me how to find k?

Answer 4

@myeyeshurt

Answer 5

@Nnesha

Answer 6

Last steps were supposed to be this*
\(k\tan\left(\frac{\frac{\pi}{2}}{k}\right)-k\tan\left(\frac{0}{k}\right)=k \) \(k\tan\left(\frac{\frac{\pi}{2}}{k}\right)=k\) \(\tan\left(\frac{\frac{\pi}{2}}{x}\right)=1\)

Answer 7

oh wait, it's 2.