A rectangular swimming pool is 44 ft wide by 75 ft long. The...

A rectangular swimming pool is 44 ft wide by 75 ft long. The table gives depths (d) from x = 0 at the shallow end to the diving end. Use the Trapezoidal Rule with n = 15 to estimate the volume of the pool, V = ?[0 to 75] 44 * d(x) dx. x | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 d | 4 | 6.2 | 7.2 | 7.9 | 8.5 | 9 | 9.5 | 9.9 | 10.3 | 10.7 | 11.1 | 11.4 | 11.7 | 12.1 | 12.4 | 12.7 The volume of the pool is ft^3. (Round to the nearest integer as needed.)

Transcript

00:01 Hello everyone, in this problem we need to estimate the volume of the pool which is given here as w0 to 75, 44 of d of x dx.

00:13 So here we are given with a rectangular swimming pool and it is of 44 feet of width and 75 feet length.

00:20 So now we are going to use trapezoidal rule with the value of n which is equal to 15 and we are given with this table of values.

00:28 So now with this values and by using the trapezoidal rule which we know as integral over a to b f of x dx will be given as del x by 2 f of x0 plus 2 multiplied by f of x1 plus f of x2 plus f of x3 plus and so on plus f of xn.

01:01 So this is the trapezoidal rule formula and we can calculate the value of del x.

01:11 So it will be given by the formula b minus a by divided by n.

01:16 So substituting its values from the given integral so here the value of b is 75 and a is 0 and n is given as 15.

01:25 So 75 minus 0 is 75, 75 divided by 15 is.

01:30 So now substituting all these values in the given trapezoidal rule formula so we get the required volume.

01:36 So the required volume v will be equal to.

01:39 So here we have taken out the constant 44 out of the integral so it will be 44 multiplied by del x by 2 is 5 by 2 multiplied by here x0 value is 4.

01:59 So here these are the values of x and the corresponding values of d of x.

02:04 The first one represents x0...

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