2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Indefinite Integrals

JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Critical Thinking

  • question_answer
    If \[x\in \left( \frac{\pi }{4},\frac{3\pi }{4} \right)\], then \[\int_{{}}^{{}}{\frac{\sin x-\cos x}{\sqrt{1-\sin 2x}}{{e}^{\sin x}}\cos x\ dx=}\]

    A) \[{{e}^{\sin x}}+c\]

    B) \[{{e}^{\sin x-\cos x}}+c\]

    C) \[{{e}^{\sin x+\cos x}}+c\]

    D) \[{{e}^{\cos x-\sin x}}+c\]

    Correct Answer: A

    Solution :

    • \[\int_{{}}^{{}}{\frac{\sin x-\cos x}{\sqrt{1-\sin 2x}}{{e}^{\sin x}}\cos x\,dx}=\int_{{}}^{{}}{\frac{\sin x-\cos x}{\sin x-\cos x}{{e}^{\sin x}}\cos x\,dx}\]
    • \[=\int_{{}}^{{}}{{{e}^{\sin x}}\cos x\,dx}={{e}^{\sin x}}+c\].


You need to login to perform this action.
You will be redirected in 3 sec spinner