I am not going to do this problem for you, but I am going to provide some hints
.First: You can look up the 2 forms of the error term and use one of them to estimate how many terms you need.
Second: The series is decreasing and has alternating signs; therefore, the error does not exceed the first omitted term. This is another way to estimate the number of terms needed.
Third: Strictly speaking the division is not "legal" since the integrand is undefined at the lower limit.