Integral Calculus
Area
MMTS_Full_Test_05
Grade 12
Question:
Area enclosed by the curve $y=\dfrac{1}{1+x^2}$ and the $x$-axis from $x=-\infty$ to $x=+\infty$ is
$\pi$
$2\pi$
$\pi/2$
$3\pi/2$
Step-by-Step Solution
Key Concept: $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}=\pi$
$[\tan^{-1}x]_{-\infty}^\infty=\pi/2-(-\pi/2)=\pi$.
Correct Answer: 2