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Approximating definite integrals Use a Taylor
Chapter 8, Problem 36E(choose chapter or problem)
QUESTION:
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 \(10^{-4}\).
\(\int_{0}^{0.1} \cos \sqrt{x} d x\)
Questions & Answers
QUESTION:
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 \(10^{-4}\).
\(\int_{0}^{0.1} \cos \sqrt{x} d x\)
ANSWER:Solution 36E
Step 1:
In this problem we need to approximate the definite integral )dx using taylor series.
We know that cos(x) = 1 - +
-
+...........
By using the above result , we get
Cos ( ) = 1 -
+
-
+...........