Question

Find \(\int_{0}^{\frac{\pi}{4}} tan^3(x)dx\).

(a) 0

(b) 1

(c) -1

(d) None of the mentioned

The question was asked in an online interview.

This is a very interesting question from Integral Reduction Formula in section Integral Calculus of Engineering Mathematics

Answer 1

Correct option is (b) 1

The best I can explain: Using the formula we have

\(\int_{0}^{\frac{\pi}{4}} tan^n(x)dx=\frac{1}{n-1}-\int_{0}^{\frac{\pi}{2}} tan^{n-2}(x)dx\)

=\(\frac{1}{2}-\int_{0}^{\frac{\pi}{4}} tan(x)dx\)

=\(\frac{1-ln(2)}{2}\)