Integration

10a - 9a^2 = 1 -->
0 = 1 - 10a + 9a^2
or 9a^2 - 1a + 1 = 0.

You probably don’t care about this anymore but it is one as you know the integration is 1 because it is stated in the question (∫upper limit 2a lower limit a (10-6x)dx=1). Therefore the integration of 20a-9a^2=1. This can then be rearranged to 9a^2-10a 1=0

I have this question:

∫upper limit 2a lower limit a (10-6x)dx=1 find two possible values of a

I first integrated 10-6x which would give me 10x-3x^2 then I inserted the lower and upper limit and took them away

10(2a)-2(2a)^2=20a-12a^2
(20a-24a^2)-(10a-3a^2)=10a-9a^2

the mark scheme tells me to rearrange equation to form quadratic equation of

9a^2-10a+1

My question is why is it 1?I know it says that this is all equal to 1 but how do we know that c is 1?

My man's going to travel back a year in time

Eh, it was mostly in case anyone else searched for the question. I got it last week and was confused by it as well. Figured I could try and explain it the way I understood it.