Grade 10Integral Calculus

options

- e^tanθ sinθ + c

e^tanθ sinθ + c

e^tanθ secθ + c

e^tanθ cosθ + c

Question image for options - e tanθ sinθ + c e tanθ sinθ + c e tanθ s

Aditya Kartikeya

11 Years agoGrade 10

1 Answer

Jitender Singh

11 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.
$(e^{tan\theta }cos\theta)' = e^{tan\theta }(-sin\theta )+cos\theta e^{tan\theta }sec^{2}\theta$
$(e^{tan\theta }cos\theta)' = e^{tan\theta }(sec\theta -sin\theta )$
$I = \int (e^{tan\theta }cos\theta )'d\theta$
$I = e^{tan\theta }cos\theta + c$