Question

\(\rm \displaystyle\int_0^1 {1\over {1 + x^2}}dx =\)
1. \(\rm {\pi\over 4}\)
2. 0
3. \(\rm {\pi\over 2}\)
4. \(\rm {\pi\over 3}\)

Answer 1

Correct Answer - Option 1 : \(\rm {\pi\over 4}\)

Concept:

\(\rm \int {1\over {1 + x^2}} dx = tan ^ {-1} x\)

Calculation:

\(\rm \displaystyle\int_0^1 {1\over {1 + x^2}}dx = [tan ^{-1}x]_{0}^{1} = [tan ^{-1}1 - tan^{-1} 0] = {\pi\over 4}\)