Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #98
Evaluate \(\int_{\pi/6}^{\pi/3}dx/(1+\sqrt{\tan x})\).
✅ Step-by-Step Solution
Final Answer: π/12
- Let I be the integral. Reflect x↦π/2−x, which interchanges the endpoints.
- Since tan(π/2−x)=1/tan x, the reflected integrand is √(tan x)/(1+√(tan x)).
- Add to get 2I=∫_(π/6)^(π/3)1dx=π/6.
- Therefore the integral equals π/12.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let I be the integral. Reflect x↦π/2−x, which interchanges the endpoints.
- [1 mark] Since tan(π/2−x)=1/tan x, the reflected integrand is √(tan x)/(1+√(tan x)).
- [1 mark] Add to get 2I=∫_(π/6)^(π/3)1dx=π/6.
- [0.5 marks] Therefore the integral equals π/12.
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