Test:351 QNo:42

iska answer options mein tha hi nahin

its answer is -pi/3

but the answer given is pi/3[11][17]

ya 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

one second it seems i misread the problem :(

step 1 put x as -x

you shall get

I=_-π∫^Ï€(xsinxcos²x)dx/2

now obsevre that f(x)=f(-x)

so this can be replaced to

2*(1/2)*₀∫^Ï€xsinxcos²dx

I=₀∫^Ï€xsinxcos²xdx

now apply x=Ï€--x

I=∫(Ï€-x)sinxcos²xdx

so we get I=(Ï€/2)₀∫^Ï€sinxcos²xdx

put cosx=t -sinxdx=dt

-(Ï€/2)₀∫^Ï€t²dt

so we get it as

I=(-Ï€/2)[t³/3]₁^-1

= (-Ï€/2)*(-2/3)=Ï€/3