integration of trig Watch

Custardcream000
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show that the area of the finite egion in the positve quadarnt bounded by the curve y =cos^3 x and the curve y = sin^3 x and the y-axis is given by (5(2)^1/2 - 4) /6,

i need help with intersection point, i think i can do the integration
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IDontEvenGoHere
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I'm currently in high school, yet my teacher sometimes gives me higher graded questions and at one of the math interventions a question similar to this came up, but I also struggled in finding the intersection point, someone please help.

sorry can't help.
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NotNotBatman
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Don't you need a domain?

For the points of intersection y=y, so

 cos^3(x) =sin^3(x)
 cos^3(x) - sin^3(x) = 0 factorise this, solve for x. Use cosx-sinx as a factor.
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Custardcream000
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(Original post by NotNotBatman)
Don't you need a domain?

For the points of intersection y=y, so

 cos^3(x) =sin^3(x)
 cos^3(x) - sin^3(x) = 0 factorise this, solve for x. Use cosx-sinx as a factor.
So you get

(cosx + sinx) (cos^2x - sin^2x) = 0

1-2sin^2x (cosx + sinx ) =0
where do i go from here?
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NotNotBatman
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(Original post by Custardcream000)
So you get

(cosx + sinx) (cos^2x - sin^2x) = 0

1-2sin^2x (cosx + sinx ) =0
where do i go from here?
That's not factorised correctly.  a^3 - b^3 = (a-b)(a^2  +ab + b^2) but finding the area above the x axis is going to be trickier as you would have the area between the two curves and between one of the curves and the point where it crosses the x axis, you also need a domain.
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