Question

Evaluate the definite integral: $∫_0^\frac{π}{4} tanxdx$

Answer 1

Let I= $∫_0^\frac{π}{4} tanxdx$

$∫tanxdx=-log|cosx|=F(x)$

By second fundamental theorem of calculus,we obtain

$I=F(\frac{π}{4})-F(0)$

$=-log|cos\frac{π}{4}|+log|cos0|$

$=-log|\frac{1}{√2}|+log|1|$

$=-log(2)\frac{1}{2}$

$=\frac{1}{2}log2$