jee-main 2023 Q72

jee-main · India · session2_10apr_shift1 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

If $I(x) = \int e^{\sin^2 x} \cos x (\sin 2x - \sin x)\, dx$ and $I(0) = 1$, then $I\!\left(\frac{\pi}{3}\right)$ is equal to
(1) $-\frac{1}{2}e^{\frac{3}{4}}$
(2) $\frac{1}{2}e^{\frac{3}{4}}$
(3) $-e^{\frac{3}{4}}$
(4) $e^{\frac{3}{4}}$

If $I(x) = \int e^{\sin^2 x} \cos x (\sin 2x - \sin x)\, dx$ and $I(0) = 1$, then $I\!\left(\frac{\pi}{3}\right)$ is equal to\\
(1) $-\frac{1}{2}e^{\frac{3}{4}}$\\
(2) $\frac{1}{2}e^{\frac{3}{4}}$\\
(3) $-e^{\frac{3}{4}}$\\
(4) $e^{\frac{3}{4}}$

Paper Questions

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