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Definite Integration — Maths STD 12 Science — Question

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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