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What is the value of 

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Detailed Solution

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Concept:

1 + tan2 x = sec2 x

Calculation:

             (∵ 1 + tan2 x = sec2 x)

Let tanx = t

Differentiating with respect to x, we get

⇒ sec2 x dx = dt

   x          0        π/4  
    t       0    1

∴ The value of the integral is 1/2.

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