Calculus Help!!

Question

let f'' = x^6-4x^4+x+1

find f(x)

Answer 1

integral of (x^6 -4x^4 + x +1)dx

= x^7/7 -4x^5/5 +x^2/2 +x + c where c= an unknown constant

just apply the power rule to each term

increase the power by 1 and divide by the resulting power

x^6 becomes x^(6+1)/(6+1)= x^7/7

do that to the other terms too, string them all together

Answer 2

Assuming the question is

f''(x) = x^6-4x^4+x+1. Find f(x).

Soln:

f’(x) = Integral f’’(x) dx. So,

f’(x) = (x^7)/7 - (4x^5)/5 +(x^2)/2 +x + c where c can be any constant

Next f(x) = Integral f’(x) dx. So,

f(x) = (x^8)/56 -(2x^6)/15+(x^3)/6 +(x^2)/2 + cx+k

where k can also be any constant.