Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\frac{\pi^2}{4}} \sin \sqrt{x} d x=$
A
$0$
B
1
✓
2
D
4
✓
Answer
Correct option: C.
2
(C) Put $x= t ^2 \Rightarrow d x=2 t dt$ When $x=0, t =0$ and when $x=\frac{\pi^2}{4}, t =\frac{\pi}{2}$ $\therefore \quad \int_0^{\frac{\pi^2}{4}} \sin \sqrt{x} d x=2 \int_0^{\frac{\pi}{2}} t \sin tdt$ $=2[-t \cos t+\sin t]_0^{\pi / 2}=2$
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