$\int_{-π/2}^{π/2} f(x) \,dx$ =? Where f(x) = sin |x| + cos |x|, x ∈ $(-\frac {π}{2}, \frac {π}{2})$

Question

$\int_{-π/2}^{π/2} f(x) \,dx$  =? Where f(x) = sin |x| + cos |x|, x ∈  $(-\frac {π}{2}, \frac {π}{2})$

cdquestions Admin · Accepted Answer

We have f(x) = sin|x| + cos|x| Then, f(x) =f(–x) Since, (f(x) is an even function. I =  $\int_{-π/2}^{π/2}sin|x| + cos|x| \,dx$ I = 2  $\int_{0}^{π/2}sin|x| + cos|x| \,dx$ I = 2[-cosx + sinx] π/2 0   I = 2[-cos  $\frac {π}{2}$  + sin  $\frac {π}{2}$  + cos 0 - sin 0]  I = 2[0 + 1 + 1–0]  I = 2x2 I = 4 Therefore, the correct option is (C) 4

Answer

Answer

Answer

Answer

\(\int_{-π/2}^{π/2} f(x) \,dx\) =?
Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)

The Correct Option is C

Solution and Explanation

Top Questions on integral

Questions Asked in MHT CET exam

\(\int_{-π/2}^{π/2} f(x) \,dx\) =?Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)

The Correct Option is C

Solution and Explanation

Top Questions on integral

Questions Asked in MHT CET exam

\(\int_{-π/2}^{π/2} f(x) \,dx\) =?
Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)