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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\frac{\pi}{2}}(x-[\cos x]) d x=$
(where [t] = greatest integer less or equal to t)
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi^2}{8}-\frac{\pi}{8}$
  • C
    $\frac{\pi^2}{8}-1$
  • ✓
    $\frac{\pi^2}{8}$
✓

Answer

Correct option: D.
$\frac{\pi^2}{8}$
(D)
Let $I =\int_0^{\frac{\pi}{2}}(x-[\cos x]) d x$
$=\int_0^{\frac{\pi}{2}} x d x-\int_0^{\frac{\pi}{2}}[\cos x] d x$
$=\left[\frac{x^2}{2}\right]_0^{\pi / 2}-0=\frac{\pi^2}{8}$

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