Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration
Let (x^2-1 ) e^x (x^2+4 x+1 ) d x=e^x f(x)+C (where C is constant of integration). If g(x)=f(x)+f^ (x) , then:
Options
- Anumber of integral roots of g(x)=0 is 2 .
- Bsum of square of integral roots of g(x)=0 is 2 .
- Cif is one non-integral root of g(x)=0 , then ^4+4 ^3+2 ^2+4 +2 is equal to 1 .
- Dg^ (0)=4 .
Correct answer
C. if is one non-integral root of g(x)=0 , then ^4+4 ^3+2 ^2+4 +2 is equal to 1 .
Step-by-step solution
Differentiating w.r.t. x , we get (x^2-1 ) e^x (x^2+4 x+1 )=e^x (f(x)+f^ (x) ) g(x)=f(x)+f^ (x)= (x^2-1 ) (x^2+4 x+1 )g(x)=0 x= 1 or x^2+4 x+1=0 array ll & ^2+4 +1=0 & Given expression = ( ^2+4 +1 ) ( ^2+1 )+1=1 . array