What will be the area which is bounded by x = 0 , y = &#x03C0;<!-- π --> <m

Flakqfqbq 2022-05-18 Answered
What will be the area which is bounded by x = 0 , y = π / 4 and y = arctan ( x )?
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Answers (2)

pomastitxz27r
Answered 2022-05-19 Author has 16 answers
The integral in the question diverges. Notice how the integrand approaches π / 2 and x . However from the comments I'm guessing you mean,
0 1 arctan x d x
(as tan π / 4 = 1) From here you can use integration by parts. Remember,
d ( arctan x ) d x = 1 1 + x 2
So, with du=1, v = arctan x u=x, d v = 1 / ( 1 + x 2 ),
0 1 arctan x d x = [ x arctan x ] 0 1 0 1 x 1 + x 2 d x
I'm assuming you can take it from here.
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Edith Mayer
Answered 2022-05-20 Author has 4 answers
The area of the figure you have described is:
0 π / 4 tan y d y = [ log | cos y | ] 0 π / 4 = 1 2 log 2.
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