(A) 0
(B) -1
(C) 1
(D) infinite
Answer: (B)
Explanation:
Let f(x) be the given function. We assume that \[\frac{1}{x} = z\]
Derivando ambos lados, obtenemos
![\[\frac{-1}{x^2} dx = dz\] Now, accordingly, the lower limit of the integral is \[ z = \frac{1}{\frac{1}{\pi}} = \pi\] and the upper limit for the integral is \[ z = \frac{1}{\frac{2}{\pi}} = \frac{\pi}{2}\] So, the given function now becomes \[ f(x)= - \int_\pi^{\frac{\pi}{2}} cos(z) dz \] \[ f(x)= \int_\frac{\pi}{2}^{\pi} cos(z) dz \] \[f(x) = sin(z) ,\] and the upper limit is π and the lower limit is π/2 So, \[f(x) = sin(\pi) - sin(\frac{\pi}{2})\] \[f(x) = 0 - 1\] \[f(x) = -1\] So, the required answer is -1.](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-02e61207a5f00fca893d03800b945e40_l3.png "Rendered by QuickLaTeX.com")
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA