Integral Calculus Question 115
Question: $ \int_{{}}^{{}}{{{\sin }^{-1}}}(\cos x)dx= $
Options:
A) $ \frac{\pi x}{2} $ + C
B) $ \frac{\pi x^{2}}{2} $ + C
C) $ \frac{\pi x-x^{2}}{2} $ + C
D) $ \frac{\pi x+x^{2}}{2} $ + C
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{{{\sin }^{-1}}(\cos x),dx}=\int_{{}}^{{}}{{ \frac{\pi }{2}-{{\cos }^{-1}}(\cos x) }},dx $ $ =\frac{\pi }{2}x-\frac{x^{2}}{2}=\frac{\pi x-x^{2}}{2} $ +C
BETA
