Mathematics-I (3110014)

Winter-2019

Question-4b-OR

BE | Semester-1 Winter-2019 | 17-01-2020

Q4) (b)

Evaluate $\int_{0}^{\infty} \frac{dx}{1 + x^{2}}$ .

$\int_{0}^{\infty} \frac{dx}{1 + x^{2}} = \lim_{b \to \infty} \int_{0}^{b} \frac{dx}{1 + x^{2}}$

$\int_{0}^{\infty} \frac{dx}{1 + x^{2}} = \lim_{b \to \infty} {[\tan^{- 1} (x)]}_{0}^{b}$

$\int_{0}^{\infty} \frac{dx}{1 + x^{2}} = \lim_{b \to \infty} [\tan^{- 1} (b) - \tan^{- 1} (0)]$

$\int_{0}^{\infty} \frac{dx}{1 + x^{2}} = \tan^{- 1} (\infty) - \tan^{- 1} (0)$

$\int_{0}^{\infty} \frac{dx}{1 + x^{2}} = \frac{π}{2}$

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Mathematics-I (3110014)

Q4) (b)

Evaluate ∫0∞dx1+x2.

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Evaluate $\int_{0}^{\infty} \frac{dx}{1 + x^{2}}$ .