The Student Room Group

urgent help needed p3! rep to be given!!!

help i need help on these two p3 june 04 questions

1) the circle C has centre (5,13) and touches the x axis

find an equation in terms of x and y for the circle c

2) using the substition u=1 + sinx and intergration show that

int. sinxcosx(1+sinx)^5 dx = (1/42)(1+sinx)^6(6sinx-1) + constant

i think ive almost done 2

have got

1/42 (6u^7 - 7u^6)


red to be given!!!
Reply 1
1) the circle C has centre (5,13) and touches the x axis

find an equation in terms of x and y for the circle c

(x - 5)^2 + (y - 13)^2 = r2

as it touches the x axis its radius must be 5 so the full equation is
(x - 5)^2 + (y - 13)^2 = 25

i think thats right :smile:
Reply 2
u = 1 + sinx
du = cosx dx

I = ∫ sinx cosx (1 + sinx)^5 dx
= ∫ (u - 1) u^5 du
= ∫ u^6 - u^5 du
= (1/7)u^7 - (1/6)u^6 + C
= (1/42) u^6 (6u - 7) + C --- You should've taken the u^6 out of the brackets.
= (1/42) (1 + sinx)^6 (6sinx - 1) + C
Reply 3
chrisgill369
1) the circle C has centre (5,13) and touches the x axis

find an equation in terms of x and y for the circle c

(x - 5)^2 + (y - 13)^2 = r2

as it touches the x axis its radius must be 5 so the full equation is
(x - 5)^2 + (y - 13)^2 = 25

i think thats right :smile:


Hate to say it but you made a mistake. As the centre is (5,13), the distance between the x axis and the centre is actually the y co-ordinate, ie 13, so the equation is....


(x - 5)^2 + (y - 13)^2 = 13^2
Reply 4
Hate to say it but you made a mistake. As the centre is (5,13), the distance between the x axis and the centre is actually the y co-ordinate, ie 13, so the equation is....


(x - 5)^2 + (y - 13)^2 = 13^2

ya you are right!!! tbh i didnt notice the mistake myself :P
Reply 5
Am I right in thinking that all circle geometry has been put in C2, and is therefore pretty easy? Like 1/2 the P3 content?
Reply 6
C4>O7
Am I right in thinking that all circle geometry has been put in C2, and is therefore pretty easy? Like 1/2 the P3 content?


i dunno but there is very little circle geometry in p3 anyway, only about 4 pages
Reply 7
Hate to say it but you made a mistake. As the centre is (5,13), the distance between the x axis and the centre is actually the y co-ordinate, ie 13, so the equation is....


woops :frown: