If is a function satisfying for all non-zero

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

f(x)

is a function satisfying

f\left(\frac{1}{x}\right) + x^2 f(x) = 0

for all non-zero

x

, then

\int_{\sin \theta}^{\csc \theta} f(x) dx

is equal to