Consider the equation _ 1 ^ e ( _ e x )^ 1 / 2 x (a- ( _ e x )^ 3 / 2 )^ 2 d x=1, a (- …
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Consider the equation
\(\int_{1}^{e} \frac{\left(\log _{e} x\right)^{1 / 2}}{x\left(a-\left(\log _{e} x\right)^{3 / 2}\right)^{2}} d x=1, a \in(-\infty, 0) \cup(1, \infty) .\)
Which of the following statements is/are true ?
\(\int_{1}^{e} \frac{\left(\log _{e} x\right)^{1 / 2}}{x\left(a-\left(\log _{e} x\right)^{3 / 2}\right)^{2}} d x=1, a \in(-\infty, 0) \cup(1, \infty) .\)
Which of the following statements is/are true ?
- No a satisfies the above equation
- An integer a satisfies the above equation
- An irrational number a satisfies the above equation
- More than one a satisfy the above equation
Answer
(C) An irrational number a satisfies the above equation
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