Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Live 1-1 coding classes to unleash the creator in your Child
Integral of xsinx/(1-cosx ) over 0 to pi Evaluate above integral problem
Dear Javed∫(x+sinx)/(1+cosx)dx => write sinx and cosx in half angle formulaes: => (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx …..........................(1) let tanx/2 = u0.5sec^2x/2 dx = duand x = vvdx = dvsubstittue in the eqn. (1)and after integrating we get,=> xtan(x/2) + c
Put x=2y integral becomes4*∫0 to pi/2 ycoty dyIntegrate by parts taking first function as y.y*lnsiny|0 to pi/2 - ∫0 to pi/2 lnsiny dy= 0 -0 - (-pi ln2)/2= (πln2)/2Note that integral of lnsinx from 0 to pi/2 is -piln2/2 (it's a solved ncert example) san also limit y tends to zero ylnsiny is equal to zero
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -