12.by gamma function,
0∫Π/2 sin8xcos8x dx
=(7*5*3*1)(7*5*3*1)/(16*14*12*10*8*6*4*2)
1.) 0∫Πsin17xcos7x dx
2.) 0∫Π/2 sin8xcos8x dx
3.) 0∫Πsin3x cos6x dx.
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13 Answers
1
11GAAMA 12 KO NAHIN AAYEGA
WAALI AND GAMMA R NOT IN THE SYLLABUS
1But it's given in JPNP n it is very useful for such sums. Even the first n third sums can be don by using it. The only thing is that u hav 2 convert it into 0∫Π/2 considering even or odd function.
1o wow bachchoooo!!!!!
yeah manipal gamma is not in syll but worth-knowing .. dats y gave these questions [5]
62I differ sky..
It is not even worth hearing
unless you are not doing it for the sake of IIT JEE but for the sake of mathematics :P
1I=\int_{0}^{\pi }{sin^{17}(x)cos^7(x)dx}\\ I=\int_{0}^{\pi }{sin^{17}(\pi -x)cos^7(\pi -x)dx}=-I \\ I=0
1as, I(x)=I(\pi -x)\\I=2\int_{0}^{\frac{\pi }{2} }{sin^{3}(x)cos^6(x)dx}\\ so\ by\ walli's\ theorem\\ I=\frac{2*2*5*3*1}{9*7*5*3*1}=\frac{4}{63}
1similarly u ca solve d first one :)
bt first one mein shyd area cancl hore hai ..........
m gettin 0 bt ......
1woh deno mein 9 aayega bhul gi likha .....aap likh do meree liye :P