Definite Integration Question 14

Question: $ \int_0^{1}{{e^{2Inx}}dx}= $

[MP PET 1990]

Options:

A) 0

B) $ \frac{1}{2} $

C) $ \frac{1}{3} $

D) $ \frac{1}{4} $

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Answer:

Correct Answer: C

Solution:

$ \int_0^{1}{{e^{2\log x}}dx=\int_0^{1}{{e^{\log x^{2}}}}dx=\int_0^{1}{x^{2}dx=[ \frac{x^{3}}{3} ]_0^{1}=\frac{1}{3}}} $ .