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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If ∫ 0 π / 4 [ tan x + cot x ] d x = π m , then the value of m is equal to

Correct answer

2

Step-by-step solution

I = ∫ 0 π / 4 [ tan x + cot x ] d x = ∫ 0 π / 4 sin x + cos x sin x cos x d x = 2 ∫ 0 π / 4 sin x + cos x 1 − ( sin x − cos x ) 2 d x Put sin x − cos x = t ( cos x + sin x ) d x = d t ∴ I = 2 ∫ − 1 0 d t 1 − t 2 I = 2 [ sin − 1 t ] − 1 0 = 2 [ 0 − ( − π / 2 ) ] = π 2 .

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