Correct Answer - Option 2 : 0
Concept:
A function, f(x) is odd if f(-x) = - f(x) and the function is even if f(-x) = f(x)
If the function is even or odd and the interval is [-a, a], we can apply these rules:
When f(x) is even:
\(\rm \int_{-a}^{a} f(x)\ dx = 2\int_{0}^{a} f(x)\ dx\)
When f(x) is odd:
\(\rm \int_{-a}^{a} f(x)\ dx =0\)
Calculation:
The given function is, f(x) = sin9x
f(-x) = sin9(-x)
= - sin9x
= - f(x)
Since the function is odd the value of \(\rm \int_{-\pi/2}^{\pi/2} sin^9x\ dx\) = 0
