GATE CS 2015 Set 3 — Question 36
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Engineering Mathematics → Calculus → Integration
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Question
The velocity (in kilometer/minute) of a motorbike which starts from rest, is given at fixed intervals of time (in minutes) as follows:
The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson’s rule is __________.
| t | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|
| v | 10 | 18 | 25 | 29 | 32 | 20 | 11 | 5 | 2 | 0 |
Correct answer
308 to 310
Solution
The motorbike starts from rest, which implies at , . We need to calculate the distance covered in 20 minutes, which is .The data points are:
Step size .
Number of intervals (even), so Simpson's 1/3 rule is applicable.Formula: Sum of ends () =
Sum of odds () =
Sum of evens () =
The distance is approximately 309.33 km.
Step size .
Number of intervals (even), so Simpson's 1/3 rule is applicable.Formula: Sum of ends () =
Sum of odds () =
Sum of evens () =
The distance is approximately 309.33 km.
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