A function y = f (x) satisfying the differential equation dy dx x… - Vidyadip

MCQ

A function $y = f (x)$ satisfying the differential equation $\frac{{dy}}{{dx}} \cdot \sin x - y \cos x + \frac{{{{\sin }^2}x}}{{{x^2}}} = 0$ is such that, $y \rightarrow 0$ as $x \rightarrow \infty$ then the statement which is correct is

A
$\mathop {Lim}\limits_{x\,\, \to \,\,0} f(x) = 1$
B
$\int\limits_0^{\pi /2} {} f(x) dx$ is less than $\frac{\pi }{2}$
C
$\int\limits_0^{\pi /2} {}f(x) dx$ is greater than unity
✓
all of the above

✓

Answer

Correct option: D.

all of the above

d
$f (x) = \frac{{\sin x}}{x}$

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