Question

Consider the following
Assertion (A): $\int \sqrt{x-3}(\sin^{-1}(\log x) + \cos^{-1}(\log x))dx = \frac{\pi}{3}(x-3)^{3/2}+c$
Reason (R): $\sin^{-1}(f(x))+\cos^{-1}(f(x))=\frac{\pi}{2}$, $|f(x)|\le 1$
The correct answer is

• A. Both (A) and (R) are true, (R) is the correct explanation of (A)
• B. Both (A) and (R) are true, (R) is not the correct explanation of (A)
• C. (A) is true, but (R) is false
• D. (A) is false, but (R) is true

Hint:

When evaluating an assertion involving an integral or a function, always check the domain of definition first. If the domain is empty, any statement about the function's value (other than possibly zero for a definite integral) is likely false.

Answer 1

The Correct Option is D