Question

For b>0 let A1 be the area bounded by x=0,x+y=1,y=bx^2 and A2 be the area bounded by y=0,x+y=1,y=bx^2 such that A1:A2=11:16 then the value of b is...

Answer 1

I came up with A1 and A2 as 11/54 and 16/54 respectively...
Bt don't know how to do it next ....
The thing that's annoying me is how to put the limits of integration for the area bound by curve and line...

Answer 2

@michele_laino

Answer 3

we have to determine the value of the parameter \(b\)

Answer 4

I know the question... Bt not the way to do that

Answer 5

I think that we can try to compute the areas A1 and A2

Answer 6

Well i found the areas...bt not in terms of that term b

Answer 7

Bcoz i don't know the intersection point of the line and the curve mentioned

Answer 8

Exactly sir! I made the diagram like that only for A1

Answer 9

we can compute the x-coordinate of the intersection point, solving this quadratic equation:
\[\Large \begin{gathered}
x + y = 1 \Rightarrow x + b{x^2} = 1 \Rightarrow \hfill \\
\hfill \\
\Rightarrow b{x^2} + x - 1 = 0 \hfill \\
\end{gathered} \]

Answer 10

U mean that in terms of square root and all..
It would be so messy then!