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## Homework Statement

i. [tex]x = 3cost,[/tex]

ii. [tex]y = 9sin2t,[/tex]

iii. [tex]0\leq t < 2\pi[/tex]

iv.[tex]\int_0^\frac{\pi}{2} Asin2tsint \ dt[/tex]

**2. The attempt at a solution**

So this is what I am given and I am supposed to be able to show that this is the integral for the shadded area between the curve and the x-axis in the 1st quadrant (sorry I know that relys on a graph, but the question is related I have isnt related to the actually shadded area anyway), so I can show the the interval is correct and form the intergral using

[tex] \int y \frac{dx}{dt} dt [/tex]

but they state as answer that A is 27. Now I know that that must be the answer because the shaded region is above the x-axis, so the integral in those limits should be possitive, but whenever I try to from the intergral equation I get -27 becuase dx/dt is -3sint. Can anyone help me to see how I have gone wrong, thanks.