Trapezium Rule

Edexcel IAL WMA12/01/P2/Oct 2019/Q5 (Trapezium Rule)

• Given 0 < a < 1​​ , sketch the curve with equation​​ 

y=ax

showing the coordinates ot- the point at which the curve crosses the y-axis.​​ 

The table above shows corresponding values of x and y for​​ y=x2 +12x​​ 

The values of y are given to 4 significant figures as appropriate.​​ 

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

• obtain an estimate for​​ ∫24x2+12xdx

(3)

Using your answer to parl (b) and making your method clear, estimate​​ 

• ∫24xx-3+12xdx

(2)

SOLUTION​​ 

a- ​​ It is given that​​ 

y=ax

Since​​ 0<a<1, it has to be a fraction. So let us suppose​​ a=12. This would give the equation to be​​ 

y=12x

y=2-1x

y=2-x

So, we need to sketch the graph of y=2-x, which is the reflection of​​ y=2x.

b-​​ 

Using Trapezium Rule to estimate​​ ∫24x2+12xdx.

(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=4-24=24=12

Now, applying the trapezium rule.​​ 

∫214log2⁡2xdx =1224.25+16.06+2 6.427+12.34

∫24x2+12xdx=19.035

∫24x2+12xdx=19.0

c-​​ 

∫24xx-3+12xdx=∫24x2+12x-3xdx

Splitting the integral so that the answer of part b can be used.​​ 

∫24xx-3+12xdx=  ∫24x2+12xdx-∫233x dx

Where​​ ∫24x2+12xdx=19.035

∫24xx-3+12xdx=19.0235-3x2224

Applying the limits

∫24xx-3+12xdx=19.0235-2422-3222

∫24xx-3+12xdx=19.0235-24-6

∫24xx-3+12xdx=19.0235-18=1.0235

∫24xx-3+12xdx=1.02