Question

The value of the integral ${\int }_a^{a+\frac{\pi }{2}}(|sinx|+|cosx|)dxis$

• A. $a\pi$
• B. $2a\pi$
• C. $\frac{a\pi }{2}$
• D. independent of a

Answer 1

The correct option is D independent of a

Since (|sin x|+|cos x|) is a periodic function with period $\frac{\pi }{2}$, therefore, ${\int }_a^{a+\frac{\pi }{2}}(|sinx|+|cosx|)dxis$ independent of a.