# Integration of Trigonometric fucntionsWatch

#1
Show that the area of the finite region in the positive quadrant bounded by the curve = cos^3 x and the curve y = sin^£ x and the y-axis is given by (5(2)^1/2 - 4)/6

what is the point where they cross

y=sin^3 x -sin^3x
i get to this:
y=(cosx - sinx)(cos^2 x + sin^2 x + cosxsinx)
(cosx - sinx)(1 + cosxsinx)

where do i go from here
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2 years ago
#2
(Original post by Custardcream000)
Show that the area of the finite region in the positive quadrant bounded by the curve = cos^3 x and the curve y = sin^£ x and the y-axis is given by (5(2)^1/2 - 4)/6

what is the point where they cross

y=sin^3 x -sin^3x
i get to this:
y=(cosx - sinx)(cos^2 x + sin^2 x + cosxsinx)
(cosx - sinx)(1 + cosxsinx)

where do i go from here
You could expand the brackets and then integrate.

It helps to know what is, and similarly for the sine.
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#3
(Original post by ghostwalker)
You could expand the brackets and then integrate.

It helps to know what is, and similarly for the sine.
Im trying to find the point where they intersect before i integrate to find area so thats what i meant where do i go from here in order to find where they intersect?
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quote
2 years ago
#4
(Original post by Custardcream000)
Im trying to find the point where they intersect before i integrate to find area so thats what i meant where do i go from here in order to find where they intersect?
Thought you'd already sorted that, as the method is completely different.

When they intersect then the two y values are equal

So,

...
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