The area bounded by the curve $y = \dfrac{1}{x^2 - 2x + 2}$ and the $x$-axis equals
Step-by-Step Solution
Key Concept: Complete the square in denominator; use standard $\int 1/(1+u^2)\,du = \tan^{-1}u$ and evaluate from $-\infty$ to $\infty$.
$\int_{-\infty}^{\infty}\frac{dx}{(x-1)^2+1} = [\tan^{-1}(x-1)]_{-\infty}^{\infty} = \frac{\pi}{2}-\left(-\frac{\pi}{2}\right) = \pi$.
Correct Answer: 4