Find the MacLaurin polynomial of degree 4 for f(x) f(x)= (integral from 0 to x) sin(3t^2) [f^(n)(0)/n!]*x^n 3. The attempt at a solution - I took the 4th derivative of sin(3t^2) and got: f''''(x)= -108sin(3t^2)-1296t^2cos(3t^2)+1296t^4sin(3t^2) Not real sure what to do from there. I plugged 0 in for t to find my f^(n)(0) and got 0,1,1,-1,-1 ...but I'm not sure if that's right. Can somebody please check my derivative and point me in the right direction for finding the series?