for the fourth q one of the roots will be zero which makes the whole integral expression zero which is independent of Î± and Î²
- Swastik Haldar thanks.Upvote·0· Reply ·2014-08-06 09:23:30
for the fourth q one of the roots will be zero which makes the whole integral expression zero which is independent of Î± and Î²
second one is x^{8}-4x^{7}+6x^{6}-4x^{5}+x^{4}1+x^{2}
divide it to simplify it
for q 5 sin[Ï€/2-(Ï€/4+x)]=sin(Ï€/4+x)
now apply the rule of definite integral âˆ«_{ba}f(x)=âˆ«_{ab}f(b+a-x) and also expand sin(x+Ï€/4) by trigonometry. then after simplifying a bit you will see that numer. and denom. is getting cancelled then putting the limits you will get the result.
for q 8 just apply the concept of integration by parts(LIATE rule) and there for the integration of x^3/âˆš(1-x^2) take x=sinÎ¸ as substitution