defn integral.......

the value of \int_{-5}^{10}{f(x)dx} if f(x)=e^{2secx}ln(1+sinx/1-sinx) if -5\leq x\leq 5
5â‰¤xâ‰¤5
f(x)=1 otherwise

2 Answers

1357

Manish Shankar ·2009-07-25 08:09:12

The function is not defined for all values of x in [-5,5]

f(-x)=e^{2sec(-x)}ln\left( \frac{1-sinx}{1+sinx}\right)=-e^{2sec}ln\left( \frac{1+sinx}{1-sinx}\right)=-f(x)

f(x) is odd so : $\int_{-5}^{5}{f(x)dx}=0$

for x>5 : f(x) = 1

\int_{-5}^{10}{f(x)dx}=\int_{-5}^{5}{f(x)dx}+\int_{5}^{10}{f(x)dx}

\int_{-5}^{10}{f(x)dx}=0+\int_{5}^{10}{1dx}

\int_{-5}^{10}{f(x)dx}=5

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