A) \[1-\frac{\pi }{4}\]
B) \[1+\frac{\pi }{4}\]
C) \[\frac{\pi }{4}-1\]
D) \[\frac{\pi }{4}\]
Correct Answer: A
Solution :
\[\int_{0}^{\pi /4}{{{\tan }^{2}}xdx=\int_{0}^{\pi /4}{({{\sec }^{2}}x-1)dx}}\] \[=\int_{0}^{\pi /4}{{{\sec }^{2}}xdx-\int_{0}^{\pi /4}{\,\,1dx}}\]= \[[\tan x]_{0}^{\pi /4}-[x]_{0}^{\pi /4}=1-\frac{\pi }{4}\].
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