Problem 33E
Approximating definite integrals Use a Taylor series to approximate the following definite integrals. Retain as many terms as needed to ensure the error is less than \(10^{-4}\).
\(\int_{-0.35}^{0.35} \cos 2 x^{2} d x\)
Step-by-Step Solution:
Solution 33EStep 1:We know the taylor series for is :Using this we get the taylor series for as followsUsing this taylor series we get the taylor series for as follows,Using this in the integral , we get The actual value of the integral is 0.69581.Error = .Hence the value of the integral using taylor series is .
Step 2 of 1
