Question

How can we integrate (1+tan^2(x)) with respect to x if the range is 0 to (pi/4)?

Answer 1

\[\int\limits_{0}^{\pi/4}(1+\tan^2(x))\] - Like this

Answer 2

[tanx + C]
[tan pi/4 - tan 0]
=1

Answer 3

helps to know that
\[1+\tan^2(x)=\sec^2(x)\] and that
\[\frac{d}{dx}\tan(x)=sec^2(x)\] so the anti derivative of
\[1+\tan^2(x)\]is
\[\tan(x)\]

Answer 4

1+tan^2 (x)=sec^2 (x)

Answer 5

Awesome explanation, satellite73. Thanks!!

Answer 6

And you too, Sarkar!