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Question

If f(0)=f(0)=0 and f′′(X)=tan2x then f(X) is

A
logsecX12X2
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B
logcosX+X22
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C
logsecX+12X2
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D
logcosXX22
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Solution

The correct option is D logsecX12X2
f′′(x)=tan2x
f(x)=tan2xdx=(sec2x1)dx=tanxx+c

f(x)=(tanxx+c)dx=logsecxx2/2+cx+d

putting f(0)=f(0)=0
c=d=0
f(x)=logsecxx22


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