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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_3^7 \sqrt{(x-3)(7-x)} d x=$
  • A
    $\pi$
  • B
    $0$
  • ✓
    $2 \pi$
  • D
    $\frac{\pi}{2}$
✓

Answer

Correct option: C.
$2 \pi$
(C)
Here, $a =3$ and $b =7$
$\int_{ a }^{ b } \sqrt{(x- a )( b -x)} d x=\frac{\pi}{8}(b- a )^2$
$\therefore \int_3^7 \sqrt{(x-3)(7-x)} d x=\frac{\pi}{8}(7-3)^2$
$=\frac{\pi}{8} \times 16=2 \pi$

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