GATE ME 2015 Set 1 — Question 13
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Engineering Mathematics → Numerical Methods → Trapezoidal & Simpson's Rules
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Question
Simpson's rule is used to integrate the function between and using the least number of equal sub-intervals. The value of the integral is ________.
Correct answer
2 to 2
Solution
Simpson's rule requires an even number of sub-intervals. The least number of sub-intervals is .
For the interval , the step size is .
The function values at the nodes are:
According to Simpson's rule:
Alternatively, since Simpson's rule is exact for polynomials of degree up to 3, we can integrate directly:
.
For the interval , the step size is .
The function values at the nodes are:
According to Simpson's rule:
Alternatively, since Simpson's rule is exact for polynomials of degree up to 3, we can integrate directly:
.
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