Trapezium Rule

Coach Name: Sir Muhammad Abdullah Shah

Edexcel IAL WMA12/01/P2/Jan 2022/Q1 (The Trapezium Rule)

The table below shows corresponding values of x and y for​​ 

y= 25-x

The values of y are given to 3 decimal places.

 

x

5

5.5

6

6.5

7

y

6.792

6.298

5.858

5.466

5.113

 

Using the trapezium rule with all the values of y in the given table,​​ 

  • obtain an estimate for​​ 

5725-xdx

giving your answer to 2 decimal places.​​ 

(3)

  • Using your answer to part (a) and making your method clear, estimate​​ 

  • 5726-xdx

  • 573+25-xdx

(4)

SOLUTION​​ 

a-​​ Using Trapezium Rule to estimate​​ 5725-xdx.

(The number of trapezium strips are 4 as we know that the number of strip is always 1 less than the total number of values of x and y given.)

h=b-an=7-54=24=0.5

A=0.526.792+5.113+26.298+5.858+5.466

A=11.78725

Answer must be 2 dp.

A=11.79

5722-xdx=11.79

b- i-​​ 5726-xdx

Applying the power rule of​​ logarithms to bring power down as the coefficient.

Applying division rule.

5726-xdx=5726÷2x.dx

Now, applying multiplication rule

5726-xdx=5721 x 25÷2x.dx

5726-xdx=572 x 25-x.dx

5726-xdx=25725-x dx

Where​​ 5722-xdx=11.79

5726-xdx=2×11.79

5726-xdx=23.5745

5726-xdx=23.57

b-ii-​​ 573+25-xdx

On splitting the integrals, we get​​ 

573+25-xdx=573dx+ 5725-x dx

Where​​ 5722-xdx=11.79

573+25-xdx=3x57+11.78725

573+25-xdx=37-35+11.78725

573+25-xdx=21-15+11.78725

573+25-xdx=17.78725 

573+25-xdx=17.79