Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

solve underroot cotx.
Asked by priyadarshini_selvam | 22 Mar, 2012, 03:53: PM
Expert Answer

Take (cot x) = t2 --> -cosec2x dx = 2t dt and we know that cosec2x =1+cot2x=1+t4

so now you have to find integration of [ 2t2/(1+t4) dt ]

= ?[(t^2 + 1) + (t^2 - 1)] / (1 + t^4) dt
= ?(t^2 + 1) / (1 + t^4) dt + ?(t^2 - 1) / (1 + t^4) dt
= ?(1 + 1/t^2) / (t^2 + 1/t^2) dt + ?(1 - 1/t^2) / (t^2 + 1/t^2) dt
= ?(1 + 1/t^2)dt / [(t - 1/t)^2 + 2] + ?(1 - 1/t^2)dt / [(t + 1/t)^2 -2]
Let t - 1/t = u for the first integral => (1 + 1/t^2)dt = du
and t + 1/t = v for the 2nd integral => (1 - 1/t^2)dt = dv
Integral
= ?du/(u^2 + 2) + ?dv/(v^2 - 2)
= (1/?2) arctan (u/?2) + (1/2?2) ln l(v -?2)/(v + ?2)l + c
= (1/?2) arctan [(t^2 - 1)/t?2] + (1/2?2) ln l (t^2 + 1 - t?2) / t^2 + 1 + t?2) + c

We get the answer by sustituting the value of t

Answered by | 22 Mar, 2012, 04:21: PM
CBSE 12-science - Maths
Asked by devilkano80 | 07 Jul, 2022, 01:45: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by dattashibani456 | 06 Apr, 2022, 01:07: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by singhdivyang308 | 07 Feb, 2022, 09:35: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by akshaytadi143 | 26 Jul, 2021, 10:30: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by anannyaratha.2004 | 19 Jul, 2021, 01:36: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
integral fraction numerator sin x times cos x over denominator square root of 1 plus sin squared end root x end fraction d x
Asked by Prajapatiraj770 | 09 Jun, 2021, 09:25: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by rajkiratsingh8800 | 23 Feb, 2021, 01:31: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Brahmduttkumar5102003 | 01 Jan, 2021, 01:44: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
integral subscript 0 superscript straight pi 1 divided by 5 plus 3 cos x
Asked by Renugarg428 | 05 Oct, 2020, 11:38: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by sidhusoni115 | 03 Oct, 2020, 08:08: AM
ANSWERED BY EXPERT

Start your hassle free Education Franchisee and grow your business!

Know more
×