Integral Calculus

Patulong po....
Find the centroid of the area bounded by the curves y=2x and y^2 =4ax using polar coordinates.

Patulong po for this problem. I really need to know the solution of this.
find the centroid of the area enclosed by the cardioid r=a(1+cos theta).

Find the centroid of the area in the first quadrant bounded by the ellipse x^2/a^2+y^2/b^2=1 and the circle x^2+y^2=a^2.

plane areas

Find the area bounded by the curve y = ln x/x, the x-axis and the maximum ordinate.

ans. 1/2

(3-x)dx/ (x^2-6x-9)^5/2

Hello, can someone help me solve this problem? I tried working it around but I can't arrive at the correct answer. Thank you!

Problem: Find the equation of the curve for which y''=12/x³ if it passes through (1,0) and is tangent to the line 6x+y=6 at that point.

Answer: xy+6x=6

Source: Elements of Calculus and Analytic Geometry by Reyes and Chua

pano po i solve to the integral of (a^2/3-x^2/3)^2/3 dx

i hope matulungan nyo po ako..salamat po .:)