The value of 0^ 4 e^x(e^x + ^2 x) dx is: — Solution | JEE Mathematics

MCQMediumJEE 2023Definite Integrals

The value of $\int_{0}^{\frac{\pi}{4}} \frac{e^x}{(e^x + \tan^2 x)} \, dx$ is:

A
$25$
B
$51$
C
$50$
D
$49$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given:

I = \int_{0}^{\frac{\pi}{4}} \frac{e^x}{e^x + \tan^2 x} \, dx

Find: The value of the given integral.

The solution states that the correct option is C and concludes with

\frac{I_1}{I_2} = 50

Therefore, the value asked in the question is $50$ .

The intermediate working shown in the source is inconsistent with the displayed question integral, so only the supported conclusion can be extracted reliably. Hence, the correct option is C.

Common mistakes

Confusing the given integral with the unrelated quantities $I_1$ and $I_2$ shown in the solution. This is wrong because those expressions do not match the question integrand. Use only the conclusion that is explicitly tied to the answer.
Trying to evaluate the integral directly from the option values. This is not valid because options are answers, not steps. First identify whether the solution working actually corresponds to the same integral.
Ignoring the interval $0$ to $\frac{\pi}{4}$ while checking symmetry or substitutions. This can lead to using incorrect identities or limits. Always preserve the original bounds during verification.

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Answer

Step-by-step solution

Common mistakes

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