NDA2021MathematicsIndefinite IntegrationActual
What is the integral of f(x)=1+x^2+x^4 with respect to x^2 ?
Options
- Ax+ x^3 3 + x^5 5 +C
- Bx^3 3 + x^5 5 +C
- Cx^2+ x^4 4 + x^6 6 +C
- Dx^2+ x^4 2 + x^6 3 +C
Correct answer
D. x^2+ x^4 2 + x^6 3 +C
Step-by-step solution
Let x^2=t aligned & f(x)=1+x^2+x^4 & I = f(x) d x^2= (1+x^2+x^4 ) d x^2 & = (1+t+t^2 ) d t=t+ t^2 2 + t^3 3 +c & I =x^2+ x^4 2 + x^6 3 +C aligned