Question

Evaluate:∫(x→0 to 1) dx/1+x^2

Answer 1

Answer:

π2.

Explanation:

We know that ∫11+x2dx=arctanx+C.

Then, by the Fundamental Principle of Definite Integral,

∴I=∫∞011+x2dx=limy→∞∫y011+x2dx

=limy→∞[arctanx]y0

=limy→∞[arctany−arctan0]

Since, the arctan fun. is continuous on R, we have,

I=arctan{limy→∞y}−0

=π2.