jee-advanced 2007 Q66

jee-advanced · India · paper1 Indefinite & Definite Integrals Integral Inequalities and Limit of Integral Sequences

Let $I = \int_0^1 \frac{\sin x}{\sqrt{x}}\,dx$ and $J = \int_0^1 \frac{\cos x}{\sqrt{x}}\,dx$. Then which one of the following is true?
(A) $I > \frac{2}{3}$ and $J > 2$
(B) $I < \frac{2}{3}$ and $J < 2$
(C) $I < \frac{2}{3}$ and $J > 2$
(D) $I > \frac{2}{3}$ and $J < 2$

Let $I = \int_0^1 \frac{\sin x}{\sqrt{x}}\,dx$ and $J = \int_0^1 \frac{\cos x}{\sqrt{x}}\,dx$. Then which one of the following is true?\\
(A) $I > \frac{2}{3}$ and $J > 2$\\
(B) $I < \frac{2}{3}$ and $J < 2$\\
(C) $I < \frac{2}{3}$ and $J > 2$\\
(D) $I > \frac{2}{3}$ and $J < 2$

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