Practicing Success
Practicing Success
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$\int_0^{π}\frac{dx}{1+3^{\cos x}}$ is equal to: |
$π$ 0 $\frac{π}{2}$ None of these |
$\frac{π}{2}$ |
$\int\limits_0^{π}\frac{1}{1+3^{\cos x}}dx=\int\limits_0^{π}\frac{dx}{1+3^{\cos(π-x)}}=\int\limits_0^{π}\frac{dx}{1+3^{-\cos x}}=\int\limits_0^{π}\frac{3^{\cos x}}{3^{\cos x}+1}dx$ $I=\frac{1}{2}\int\limits_0^{π}(\frac{1+3^{\cos x}}{1+3^{\cos x}})dx=\frac{π}{2}$ |
