For x ∈ (-π/2, π/2), if y(x) = ∫ (csc x + sin x)/(csc x sec x + tan x sin² x) dx and lim_(x → (π/2)⁻) y(x) = 0…

Question

For $$x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$$, if $$y(x) = \int \frac{\csc x + \sin x}{\csc x \sec x + 	an x \sin^2 x}\, dx$$ and $$\lim_{x 	o \left(\frac{\pi}{2}ight)^-} y(x) = 0$$, then $$y\left(\frac{\pi}{4}ight)$$ is equal to:

Accepted Answer

D. $$\left(\frac{1}{\sqrt{2}}ight) 	an^{-1}\left(-\frac{1}{2}ight)$$

Answer

A. $$	an^{-1}\left(\frac{1}{\sqrt{2}}ight)$$

Answer

B. $$\left(\frac{1}{2}ight) 	an^{-1}\left(\frac{1}{\sqrt{2}}ight)$$

Answer

C. $$-\left(\frac{1}{\sqrt{2}}ight) 	an^{-1}\left(\frac{1}{\sqrt{2}}ight)$$

Answer & step-by-step solution

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