Question

I have to evaluate the integral of x=0 to x=pi/3 of

(1-sin(x))/cos(x)) du

Te answer that i found is: ln|2+sqare root of 3| - ln|2| but the actual answer is ln(2+sqare root of 3). What did i do wrong?

Answer 1

i guess you used u substitution for one of the expressions? what are you new limits of integration?

Answer 2

Sec x - tanx

Answer 3

\[\int\limits \frac{1-sinx}{cosx}dx= \int\limits (1-sinx)secxdx\]

Answer 4

\[\int\limits (1-sinx)secxdx = \int\limits (secx-tanx)dx= \int\limits secx dx - \int\limits tanx dx\]

Answer 5

\[\int\limits \tan(x) dx = - \ln(\cos(x))+c\]

Answer 6

\[\int\limits \sec(x)dx = \ln(\tan(x)+\sec(x))+c\]

Answer 7

\[ \ln(\cos(x))+\ln(\tan(x)+\sec(x))+c\]

Answer 8

now u may plug in ur values to check the answers...