Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

806,708 users

Find the definite integral,

0 votes
Find the definite integral,

∫ (from pi/2 to pi) sin(x)/1+cos^2(x)
asked Sep 15, 2018 in CALCULUS by anonymous
edited Sep 17, 2018 by bradely

1 Answer

0 votes

Calculate the ∫ (from pi/2 to pi) sin(x)/1+cos^2(x).

First find the ∫ sin(x)dx/1+cos^2(x).

Let cosx =t

dt/dx =-sinx

-dt =sinx dx

∫ sin(x)dx/1+cos^2(x). =∫ -dt/1+t^2

                                 =-tan^-1(t)

                                 =-tan^-1(cosx)

Calculate the definite integration using the fundamental theorem of intehration.

∫ (from pi/2 to pi) sin(x)/1+cos^2(x).=(from pi/2 to pi)( -tan^-1(cosx))

                                                     =-[tan^-1(cospi/2)-tan^-1(cospi)]

                                                     =-[0-(tan^-1(-1)]

                                                     =-(-pi/4)

                                                     = pi/4

answered Sep 17, 2018 by lilly Expert

Related questions

asked Apr 20, 2015 in CALCULUS by anonymous
asked Nov 26, 2014 in CALCULUS by anonymous
...