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Calculus Level 5

f ( x ) = x − 3 ( arcsin ⁡ ( ln ⁡ ( x ) ) + arccos ⁡ ( ln ⁡ ( x ) ) ) f(x) = \sqrt{x-3} \ ( \arcsin ( \ln (x)) + \arccos (\ln (x) ))

Integrate f ( x ) f(x) with respect to x x .

π 4 ( x − 4 ) 3 / 2 + C o n s t a n t \frac \pi4 (x-4)^{3/2} + \ Constant π 3 ( x − 3 ) 3 / 2 + C o n s t a n t \frac \pi3 (x-3)^{3/2} + \ Constant 0 None of these choices arcsin ( ln ⁡ ( cos ⁡ ( x ) ) + C o n s t a n t \text{arcsin}(\ln(\cos(x)) + \ Constant

Mayank Singh by Mayank Singh , 22, India

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1 solution

Mayank Singh
Jul 10, 2015

First of all lets check the domain of f(x)

For f(x) to be defined x>=3 and mod(x) <=e,which can't be true simultaneously. Hence anti derivative of f(x) doesn't exist.

9 Helpful 0 Interesting 0 Brilliant 0 Confused

This is more like a trick question, wherein people will just blindly see the answer that seems absolutely correct, and get it wrong, like I did. Nice ;)

Sanchit Aggarwal - 5 years, 11 months ago

no need to write mod (1/e)<x<e and x>3 which can't be true simultaneously

Akul Agrawal - 5 years, 11 months ago

Nice question

Prakhar Bindal - 5 years ago

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i no ........................................

Mayank Singh - 5 years ago

the problem did not state f(x) is real. if you assume complex valued integral than (a) is correct

Ilya Lyubarsky - 2 years, 3 months ago

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