Question

Consider the equation $\int\limits_1^e \frac{\left(\log _{ e } x \right)^{1 / 2}}{x\left(a-\left(\log _{ e } x \right)^{3 / 2}\right)^2} dx =1, \quad a \in(-\infty, 0) \cup(1, \infty)$ Which of the following statements is/are TRUE ?

• A. No $a$ satisfies the above equation
• B. An integer $a$ satisfies the above equation
• C. An irrational number $a$ satisfies the above equation
• D. More than one $a$ satisfy the above equation

Answer 1

Answer: (C), (D)

An irrational number $a$ satisfies the above equation

Answer 2

(C) An irrational number a satisfies the above equation

(D) More than one a satisfy the above equation