Integral Calculus Question 269
Question: $ \int_{{}}^{{}}{({{\sin }^{-1}}x+{{\cos }^{-1}}x)\ dx=} $
[MP PET 1990]
Options:
A) $ \frac{1}{2}\pi x+c $
B) $ x({{\sin }^{-1}}x-{{\cos }^{-1}}x)+c $
C) $ x({{\cos }^{-1}}x+{{\sin }^{-1}}x)+c $
D) $ \frac{\pi }{2}+x+c $
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Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{({{\sin }^{-1}}x+{{\cos }^{-1}}x),dx}=\int_{{}}^{{}}{( \frac{\pi }{2} )},dx=\frac{\pi x}{2}+c $ $ ( \because ,{{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} ) $ Also $ \int_{{}}^{{}}{({{\sin }^{-1}}x+{{\cos }^{-1}}x)dx=x({{\cos }^{-1}}x+{{\sin }^{-1}}x)+c} $ .
BETA
