29\int_{0}^{\Pi /4}({tan^{n-2}+tan^{n})\frac{d}{dx}}
if this is the question then the answer is 1/n-1
5 Answers
29
1\int_{0}^{\Pi /4}(({tan^{n-2}x+tan^{n}x)\frac{d}{dx}(x-[x]-[x]^{2}-[x]^{3})})dx
here's the question
1@govind.... itz only a half of the questn...
bt still u gt d correct ans...lol,....:)
29kk i got it correct bcoz [x] wen x ε (0,pi/4) is 0 ...so all terms will get canceled and u will get the integral that i posted in #2 ..sry a li'l correction in post 2 ..that will be \int_{0}^{\Pi /4}({tan^{n-2}+tan^{n})dx } = \frac{1}{n-1}
1yes in limits 0 to π/4 [x] is 0 so it is eliminated and left is differentiation of x and given expression in tan form.
whose integration can be found by reduction formula
[1] so will get answer wat govind has mentioned [1]