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options - e tanθ sinθ + c e tanθ sinθ + c e tanθ secθ + c e tanθ cosθ + c

options
  1. - etanθ sinθ + c
  2. etanθ sinθ + c
  3. etanθ secθ + c
  4. etanθ cosθ + c

Question Image
Grade:10

1 Answers

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

I = \int e^{tan\theta }(sec\theta - sin\theta )d\theta
Apply the rule that integration is a reverse process of differentiation.
(e^{tan\theta }cos\theta)' = e^{tan\theta }(-sin\theta )+cos\theta e^{tan\theta }sec^{2}\theta
(e^{tan\theta }cos\theta)' = e^{tan\theta }(sec\theta -sin\theta )
I = \int (e^{tan\theta }cos\theta )'d\theta
I = e^{tan\theta }cos\theta + c

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