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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
If I(x)=∫esin⁡2x(cos⁡xsin⁡2x−sin⁡x)dxI(x)=\int e^{\sin ^2 x}(\cos x \sin 2 x-\sin x) d x and I(0)=I(0)= 1 , then I(π3)I\left(\frac{\pi}{3}\right) is equal to
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Correct option: B
12e34\frac{1}{2} e^{\frac{3}{4}}
Option B (12e34\frac{1}{2} e^{\frac{3}{4}}) is correct because it involves solving the given integral and applying the initial condition.

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