Find f. (Use C for the constant of the first antiderivative, D for the constant of the second antiderivative and E for the constant of the third antiderivative.)

Question

f'''(x) = sqrt(t) - 6 cos t, determine f(x)

Answer 1

f"'(t) = ∫f''''(t)dt = (2/3)t^3/2 - 6sint + C

f'(t) = ∫f"(t)dt = (4/15)t^5/2 + 6cost + Ct + D

f(t) = ∫f'(t)dt = (8/105)t^7/2 + 6sint + (C/2)t² + Dt + E