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Question

The area of the region bounded by the curve y=11+(tanx)2 and the xaxis between the ordinates x=π6 and x=π3 is π12 sq units.

A
True
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B
False
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Solution

The correct option is A True
The given curve is y=11+(tanx)2
y=(cosx)2(sinx)2+(cosx)2
Area bounded between the intervals x=π6 and x=π3 is given by
A=π3π6(cosx)2(sinx)2+(cosx)2dx
Also A=(sinx)2(sinx)2+(cosx)2
Adding we get
2A=π3π6dx
A=12π3π6dx

=12[x]π3π6

=12[π3π6]

=π12.sq.units.

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