WMA11 October 2022

2. WMA11/01 (Edexcel) IAL P1 October 2022, Q2, Integration

Given that​​ 

(x – 5)(2x + 1)(x + 3) ≡ ax3 + bx2 –32x – 15 

where a and b are constants,​​  

(a) find the value of a and the value of b.​​ 

(2)

(b) Hence find​​ 

∫x-52x+1x+35xdx

writing each term in simplest form.​​ 

(5)

SOLUTION

a- The constant ‘a’ is the coefficient of x2​​ and ‘b’ is the coefficent of x.

x – 52x + 1x + 3=x-52x2+6x+x+3

=x-52x2+7x+3

=2x3+47+3x-10x2-35x2-15

=2x3-3x2-32x-15

On comparing teh above expression with ax3 ​​​​ + bx2​​ – 32x – 15. ​​ 

a=2

b=-3

b-​​ 

Always remember, when the word ‘’hence’’ is used in the question, it means we have to use the answer of prevous part and carry the calculations out for the next part of it.​​ 

∫x-52x+1x+35xdx

=∫2x35x12-3x25x12-32x15x12-155x12d

=∫25x52-35 x32-325x12-3x-12dx

=25×x7272-35×x5252-325×x3232-3×x1212+c

=27 x25 x72 -25 x35x52-23 x 325x32-2 x 3x12+c

∫x-52x+1x+35xdx=435x72-625 x52-6415x32-6x12+c