c4 jan 06 intergration question im sure MS is wrong !! paper and MS for those who nee

ok heres the problem

Using the substitution u2 = 2x – 1, or otherwise, find the exact value of

I=3x/(2x-1)^0.5

its question 3.

igot 3x/4(2x-1)^0.5 could anyone confirm this

vestor question thanks

The line l1 has vector equation

r = 8i + 12j + 14k + t(i + j – k),

where t is a parameter.
The point A has coordinates (4, 8, a), where a is a constant. The point B has coordinates (b, 13, 13), where b is a constant. Points A and B lie on the line l1.

(a)Find the values of a and b.

c4jan06.doc90.6KB

c4jan06MS.doc249.3KB

Reply 1

SunGod87

u^2 = 2x - 1
u = (2x - 1)^(1/2)
du/dx = (2x - 1)^(-1/2)
2x = u^2 + 1
3x = (3/2)(u^2 + 1)

Limits:
x = 5, u = 3
x = 1, u = 1

Transforming the integral into:

I = (3/2)u^2 + 3/2
Which integrates to 1/2u^3 + 3/2u

Putting in limits:

= [1/2((3)^3) + (3/2)(3)] - [1/2((1)^3) + 3/2(1)]
= (13.5 + 4.5) - (0.5 + 1.5)
= 18 - 2
= 16

Mark scheme is correct.

Reply 2

joe8232

I have attached a quick solution to this question - so it may not be 100% perfect but it the method is there. Hope it helps. For the second question put the x,y,z value equal to its components in the equation given i.e. 8+t = 4, 12+t=8, these give consistent values of t (-4) then put this value in to find z so 14 -4t - a repeat this for b.

Picture 1.png10.6KB

Reply 3

investor

thanks all anyone for the vectors question have some pos rep both of yolu

Reply 4

joe8232

Since you know that both points lie on the line. This means that for the first point:
comparing values of i,j,k:
8+t=4 => t=-4,
12+j=8 => t=-4, therefore a = 14 + 4 = 18

just do the same then with the other one to find b.