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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^1 \frac{d x}{x^2-2 x+2}=$
  • A
    $\frac{\pi}{2}$
  • B
    $-\frac{\pi}{2}$
  • ✓
    $\frac{\pi}{4}$
  • D
    $-\frac{\pi}{4}$
✓

Answer

Correct option: C.
$\frac{\pi}{4}$
(C)
$\int_0^1 \frac{d x}{x^2-2 x+2}=\int_0^1 \frac{d x}{(x-1)^2+1}$
$\begin{array}{l}=\left[\tan ^{-1}(x-1)\right]_0^1 \\ =0-\left(-\frac{\pi}{4}\right)=\frac{\pi}{4}\end{array}$

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