₅^9 3 x^2 3 x^2+ (588-84 x+3 x^2 ) d x is equal to

Step-by-step solution

Let I= ₅^9 3 x^2 d x 3 x^2+ (588-84 x+3 x^2 ) ...(i) aligned & = ₅^9 3 x^2 d x 3 x^2+ 3(14-x)^2 & = ₅^9 3(14-x)^2 d x 3(14-x)^2+ 3(14-(14-x))^2 & [ _a^b f(x) d x= _a^b f(a+b-x) d x ] aligned I= ₅^9 3(14-x)^2 d x 3(14-x)^2+ 3 x^2 ...(ii) Adding Eqs. (i) and (ii), we get aligned & 2 I= ₅^9 3 x^2+ 3(14-x)^2 3(14-x)^2+ 3 x^2 d x & 2 I = ₅^9 d x=9-5=4 I=2 aligned