GATE2007-IT-22

Question

The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$.  Consider the following values for the step size h.

1. 10^-2
2. 10^-3
3. 10^-4
4. 10^-5

For which of these values of the step size h, is the computed value guaranteed to be correct to seven decimal places. Assume that there are no round-off errors in the computation.

• A. iv only
• B. iii and iv only
• C. ii, iii and iv only
• D. i, ii, iii and iv

Answer 1

error = (b-a)h².max(f"(x) between 0 and 1) /12 

error <= 10^-7

solving these equations we get

h <= 6.644*10^-4

option B

Comments

@Vikrant : why error <=10^-8

Why not 10^-7 ??

We need only upto 7 decimal places !!

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@sandeep you are right it should be 10^-7. I have edited the answer.