jee-advanced 2014 Q42

jee-advanced · India · paper2 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression)

The following integral
$$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2\operatorname{cosec} x)^{17}\, dx$$
is equal to
(A) $\int_{0}^{\log(1+\sqrt{2})} 2\left(e^{u} + e^{-u}\right)^{16} du$
(B) $\int_{0}^{\log(1+\sqrt{2})} \left(e^{u} + e^{-u}\right)^{17} du$
(C) $\int_{0}^{\log(1+\sqrt{2})} \left(e^{u} - e^{-u}\right)^{17} du$
(D) $\int_{0}^{\log(1+\sqrt{2})} 2\left(e^{u} - e^{-u}\right)^{16} du$

The following integral

$$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2\operatorname{cosec} x)^{17}\, dx$$

is equal to\\
(A) $\int_{0}^{\log(1+\sqrt{2})} 2\left(e^{u} + e^{-u}\right)^{16} du$\\
(B) $\int_{0}^{\log(1+\sqrt{2})} \left(e^{u} + e^{-u}\right)^{17} du$\\
(C) $\int_{0}^{\log(1+\sqrt{2})} \left(e^{u} - e^{-u}\right)^{17} du$\\
(D) $\int_{0}^{\log(1+\sqrt{2})} 2\left(e^{u} - e^{-u}\right)^{16} du$

Paper Questions

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