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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\frac{\pi}{4}} \sin (x-[x]) d (x-[x])$ is equal to
  • A
    $\frac{1}{2}$
  • ✓
    $1-\frac{1}{\sqrt{2}}$
  • C
    1
  • D
    None of these
✓

Answer

Correct option: B.
$1-\frac{1}{\sqrt{2}}$
(B)
$\int_0^{\frac{\pi}{4}} \sin (x-[x]) d (x-[x])$
$=\int_0^{\frac{\pi}{4}} \sin (x-0) d (x-0)$
$=\int_0^{\frac{\pi}{4}} \sin x d x$
$=[-\cos x]_0^{\pi / 4}=-\cos \frac{\pi}{4}+\cos 0=1-\frac{1}{\sqrt{2}}$

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