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Integrate ∫((tanx) 1/2 +(cotx) 1/2 ) dx

Integrate
∫((tanx)1/2+(cotx)1/2) dx

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int [\sqrt{tanx} + \sqrt{cotx}]dx
I = \int [\sqrt{\frac{sinx}{cosx}} + \sqrt{\frac{cosx}{sinx}}]dx
I = \int \frac{sinx + cosx}{\sqrt{sinx.cosx}}dx
sinx - cosx = t
(cosx + sinx)dx = dt
(sinx -cosx)^{2} = t^{2}
1 - 2sinx.cosx = t^{2}
sinx.cosx = \frac{1-t^{2}}{2}
I = \int \frac{\sqrt{2}}{\sqrt{1-t^{2}}}dt
I = \sqrt{2}sin^{-1}t + c
I = \sqrt{2}sin^{-1}(sinx -cosx) + c
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

Please see the solution in the attachment.
643-1382_Untitled.png
I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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