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Dear Student,
GDB  starting date : 17 august 2015 ;  closing date: 18 august 2015    . The question is as under:

A train is moving at the speed of 30 m/sec. Suddenly brakes are applied. The speed of the train per second after t seconds is given by

 Time(t) 0 5 10 15 20 25 30 35 40 45 Speed(s) 30 24 19 16 13 11 10 8 7 5

Which quadrature rule is used to determine the distance moved by the train in 45 seconds and why?

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### Replies to This Discussion

plz sir help $\begin{gathered} let\,s\,be\,the\,dis\tan ce\,\,travelled\,by\,in\,ts\,then, \hfill \\ \,\frac{{ds}} {{dt}} = v \hfill \\ so \hfill \\ [s]^{45} _{t = 0} = \int\limits_0^{45} {vdt} \hfill \\ \hfill \\ \int\limits_0^{45} {vdt} = \frac{{15}} {8}[(v_0 + v_9 ) + 3(v_1 + v_2 + v_4 + v_5 + v_7 + v_8 ) + 2(v_3 + v_6 )] \hfill \\ \int\limits_0^{45} {vdt} = \frac{{3h}} {8}[(30 + 5) + 3(24 + 19 + 13 + 11 + 8 + 7) + 2(16 + 10)] \hfill \\ = 624.375m \hfill \\ \hfill \\ \end{gathered}$

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"Simpson's Method for double integrals

In train example, when breaks are applied on train, then train velocity of train became decrease, and at last it stopped. Now one point when train velocity became slow can say x. When train is stopped means at zero velocity, it is second point can say y.

Here x = 30 m/sec and y = 0 m/sec. then we find distance covered in zero to 45 sec by the train.

This is Simpson's Method for double integrals

Double Integral of F from 30 to zero.

This is called Gaussian quadrature for double integrals"