Find the smallest n such that the error estimate in the approximation of the definite integral $\int _ { 0 } ^ { 1 } 2 \sin \left( x ^ { 2 } \right) d x$ is less than $0.00001$ using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative.
A) 208
B) 189
C) 196
D) 201
E) 188

Question

Quizplus · Accepted Answer

The error in the Trapezoidal Rule is given by $\frac{(b-a)^3}{12n^2} \max |f''(x)|$. Estimating $|f''(x)|$ and solving for $n$ gives the smallest $n$ as 196.

Find the Smallest N Such That the Error Estimate in the Approximation