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What is the integral of (1-sec x)^1/2? Please tell me fast its urgent hurry up

What is the integral of (1-sec x)^1/2? Please tell me fast its urgent hurry up

Grade:12

1 Answers

Ritika Das
105 Points
6 years ago
 
Let u = 1 – sec x.
du/dx= – sec x.tan x.
dx=( – 1/sec x.tan x).du.
Now, I=∫sqrt.(1 – sec x).dx.
Putting values from above we get: – 
          =∫sqrt.(u).du.( – 1/(sec x.tan x)).
          = – 1/(sec x.tan x)∫u1/2.du.
          = – 1/(sec x.tan x).(2/3).u3/2 + c.
Putting back value of u we get the final answer: – 
I = – 2/(3sec x.tan x).(1+sec x)3/2 + c.
Please approve my answer if you like the explanation!

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