Find the most general f. Use C for the constant of the first anti-derivative and D for the constant of the second anti-derivative.

f ''(x) = 4x + sin x

Question

Find the most general f. Use C for the constant of the first anti-derivative and D for the constant of the second anti-derivative.

f ''(x) = 4x + sin x

myininaya · Answer

$$\int\limits_{}^{}f''(x) dx=f'(x)+C$$
$$\int\limits_{}^{}(f'(x)+C)dx=f(x)+Cx+D$$
where C and D are constants
so to find f you need to find f' first

anonymous · Answer

thank you for the procedure, myininaya.  Do you have an answer?

myininaya · Answer

$$f'(x)=4*\frac{x^{1+1}}{1+1}-cosx+C$$

$$f'(x)=2x^2-cosx+C$$

$$f(x)=2*\frac{x^{2+1}}{2+1}-sinx+Cx+D$$

anonymous · Answer

Er...is it supposed to be "x^2+1" or did you intentionally write the numerator with "2+1" as the exponent for x?

myininaya · Answer

yes 2+1 is the exponent

myininaya · Answer

$$f(x)=2*\frac{x^3}{3}-sinx+Cx+D$$
i was just showing you what rule i was using to integrate(showing you my work)

myininaya · Answer

hipster do you got it?

anonymous · Answer

Yep I got it.  Thanks :)