Multiple choice

The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is

  1. 1000e

  2. 1000

  3. 100e

  4. 100
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A Correct answer
Explanation

Trapezodial rule is $\int_{x_0}^{x_0 + nh}dx =\dfrac{h}{2}[(y_0 + y_n) + 2(y_1 + y_2 + .... + y_{n-1})]$ $\int_{1}^{2}xe^xdx ]$ = 1000e

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