1ya itz pi/3 aata hai
arey I +I use kar......... phir halvin d inetrval kar.......
phir cos@ =t dal
phir
phir
phir.....................
answer nikal
pi/3 aata hai ji
\int_{-\pi }^{\pi }{\frac{xsinxcos^{2}xdx}{e^{x}+1}}
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4 Answers
11iska answer options mein tha hi nahin
its answer is -pi/3
but the answer given is pi/3[11][17]
1
1one second it seems i misread the problem :(
step 1 put x as -x
you shall get
I=-π∫π(xsinxcos2x)dx/2
now obsevre that f(x)=f(-x)
so this can be replaced to
2*(1/2)*0∫πxsinxcos2dx
I=0∫πxsinxcos2xdx
now apply x=Ï€--x
I=∫(π-x)sinxcos2xdx
so we get I=(π/2)0∫πsinxcos2xdx
put cosx=t -sinxdx=dt
-(π/2)0∫πt2dt
so we get it as
I=(-Ï€/2)[t3/3]1-1
= (-Ï€/2)*(-2/3)=Ï€/3