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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^\pi \frac{d x}{1+\sin x}=$
  • A
    $0$
  • B
    $\frac{1}{2}$
  • ✓
    2
  • D
    $\frac{3}{2}$
✓

Answer

Correct option: C.
2
(C)
$\int_0^\pi \frac{ d x}{1+\sin x}=\int_0^\pi \frac{1-\sin x}{\cos ^2 x} d x$
$\begin{array}{l}=\int_0^\pi\left(\sec ^2 x-\sec x \tan x\right) d x \\ =[\tan x-\sec x]_0^\pi \\ =\tan \pi-\sec \pi+1 \\ =0+1+1=2\end{array}$

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