Final Answer
$\frac{\pi}{2}$
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Step-by-step Solution
Problem to solve:
$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$
Specify the solving method
1
Solve the integral by applying the formula $\displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right)$
$\left[\arctan\left(x\right)\right]_{0}^{\infty }$
2
Replace the integral's limit by a finite value
$\lim_{c\to\infty }\left(\left[\arctan\left(x\right)\right]_{0}^{c}\right)$
Learn how to solve definite integrals problems step by step online.
$\left[\arctan\left(x\right)\right]_{0}^{\infty }$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/(1+x^2) from 0 to \infty. Solve the integral by applying the formula \displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right). Replace the integral's limit by a finite value. Evaluate the definite integral. Simplifying.
Final Answer
$\frac{\pi}{2}$
Numeric Answer
$1.570796$