Question

Find the particular solution for the anti-derivative of f'(x) = 2x^3 + 1 – sin x, if f(0) = 1.

Answer 1

\[f(x)=x^4/2+x+cosx+C\]and,\[f(0)=(0/2)+(0)+\cos0+C=1+C\]Sine f(0)=1, the constant C=0. So \[f(x)=x^4/2+x+cosx\]