Question

The value of integral $\int [\sin x+\cos x]dx$ will

• A. $x+c$ if $x\in (0,t),t\in (0,\frac{\pi }{2})$
• B. $[-\cos x+\sin x]\forall x\in (\frac{\pi }{2},\pi )$
• C. Some constant if $x\in (0,t),t\in [0,\frac{\pi }{2}]$
• D. $[-\cos x+\sin x]\forall x\in (0,\frac{\pi }{2})$

Answer 1

Answer: (A)

$x+c$ if $x\in (0,t),t\in (0,\frac{\pi }{2})$

Given : $\int [\sin x+\cos x]dx$

We know for $x\in [0,\frac{\pi }{2}]$ both $\sin x$ & $\cos x$ are positive.

And $\sin x+\cos x>1$ For $x\in [0,\frac{\pi }{2}]$

${\int }_0^x[\sin x+\cos x]dx={\int }_0^{x}dx=x$

For $x\in (0,t)t\in (0,\frac{\pi }{2})$