its the last question in the last book so its lengthy, and not specific to one thing,(adsbygoogle = window.adsbygoogle || []).push({});

anyway a curve (that looks like an infinity symbol) is given by

x = 3cost and y = 9sin2t, 0≤t<2pi

a) find the cartesian in form y^2 = f(x)

i done that no problem and got y^2 = 4x^2(9-x^2)

b) show the shaded area enclosed by the curve and the x axis is given by

[tex]\int_{0}^{\frac{\pi}{2}}Asin2t sint dt[/tex]

stating the value of A

the infinity sign shaped curve is cut in half horizontally by the x axis, (and vertically by the y and by itself) the shaded sector is the top right one.

as the area = ∫ydx

y = 9sin2t

dx/dt = -3sint

so dx = -3sintdt

therefore area = ∫(9sin2t)(-3sintdt)

= ∫ -27sin2tsintdt

so A = -27

but the answer gives +27...

if i took +27 as my answer i can get the rest of the question right, but i get minus which doesnt make sense

if you need the diagram clarified i can draw it if you wish

thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Last integration question in the book

**Physics Forums | Science Articles, Homework Help, Discussion**