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can tan theeta be integrated?

can tan theeta be integrated?

Grade:8

5 Answers

Neha Gaur
6 Points
8 years ago

integration of tan theeta is log|sec theeta| +constant

Godfrey Classic Prince
633 Points
8 years ago

Dear R VISWANANTH,

Yes ofcourse. Tanθ can be integrated.

∫tanθ = -ln|cosθ| + C

where C is the Integral Constant .

 

Hope this helped you immensely..!

All the Very Best & Good Luck to you ..!!

 

Best Regards,

AskIITians Expert,

Godfrey Classic Prince

IIT-M

Please approve my answer if you liked it by clicking on "Yes" given below..!!Smile


 

sparsh shrivastava
19 Points
8 years ago

yes you can intergrate tan theeta.

 

tan q = sin q/cos q (1)

let,

y = cos q

so, dy/dq = -sin q

this implies, dq=dy/-sin q  (2)

 

putting values in (1)

∫ 1/-y 

= -log|y|

=-log|cos q|

 

so the ∫ tan q = -log|cos q|

himanshu saini
31 Points
8 years ago

yes     log|tantheeta +sectheeta|


VAISHNAVI SATHYA
16 Points
8 years ago

s u can integrate tanθ

write tanθ=sinθ/cosθ

so now, integral of tanθ.dθ=integral of sinθ/cosθ.dθ→1

put cosθ=t→2

there fore -sinθ.dθ=dt→3

put 2 and 3 in 1

so,the question becomes integral of tanθ.dθ=integral of -dt/t→4

=-log t +c      →   5                  [reason:dx/x=logx]

put 2 in 5,

 

=-log cosθ+C

where C is the integration constant

 


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