I got a curve y = n ( 16-x2 )
Now the question is to find 'n' when the area between the curve and x axis is 33.
how would i go about it?
think basic. how do we find the area between the curve and the axis?
$\displaystyle y = n \left( 16 - x^2 \right)$
where does y meet the x-axis? that is, when is y zero?
$\displaystyle \Rightarrow 0 = n \left( 16 - x^2 \right) $
$\displaystyle \Rightarrow 0 = 16 - x^2$
$\displaystyle \Rightarrow 0 = (4 + x)(4 - x)$
$\displaystyle \Rightarrow x = \pm 4$
So we want: $\displaystyle A = n \int_{-4}^{4} \left( 16 - x^2 \right)~dx = 2n \int_{0}^{4} \left( 16 - x^2 \right)~dx = 33$
now continue...
no. the integral of 16 with repsect to x is 16x.
remember, $\displaystyle \int cx^n~dx = \frac {cx^{n + 1}}{n + 1} + C$
we can think of $\displaystyle 16$ as $\displaystyle 16x^0$
so to integrate a constant, we just attach the variable we are integrating with respect to
anyway, now continue