12. Ap Calc Help AnyOne?

Question

the total area of the region bounded by the graph of y=x sq. rt ( 1-x^2) and the x-axis is

Answer 1

You need: Integral of x sqrt(1-x^2) dx.

The best way to do this is by letting z = 1-x^2. Then you have
dz = -2x dx.

This allows you to change the integral to:

Integral of ( - 1/2 ) sqrt(z) dz which immediately integrates to:

(-1/2)(2/3) z^(3/2) = (-1/3) (1-x^2)^(3/2)

I'm ignoring the constant of integration. Anyway, this integral, evaluated between any two x values, gives you the area in between your curve & the x axis.

Answer 2

integrate? the boundaries are -1 to 1
or you could use 0 to 1 then multiply to 2

the graph is symmetrical on the origin.. the reason u cud multiply it to 2 .. if you use the boundaries 0->1

Answer 3

y=0 is
x axis

0=x(sqrt(1-x^2)

x=0
x=-1
x=1

calculate the integral:
x=1
2 * ∫xsqrt(1-x^2)dx=?
x=0