Recent content by Noriele Cruz

We were taught of several integration technique, only to find one of those techniques came up as years of solving of our professor.. Can someone explain to me how substitution x = 1 / z dx = -dz / z^2 works for some problems? He called this reciprocal substitution, as what you can literally...

How about the curve in the part of the sector? If I'm not mistaken, the figure you posted is somehow a triangle rather than a sector with curve part. Where is it?

How come my picture of my integration of sector can be drawn like this? Is this also the same with mine?

Nonetheless, it is a basic format on how to factor such kind of expressions. It's not a point of remembering a trick, it is one way of knowing a proof how such expression can be branched down into its respective factors.

Have you checked my solution in the attached file? For the formula A = 1/2 sr, how it was derived using integration? Sorry for so many questions, I just want to clear up my mind.

There's a trick in factoring (a3 - b3) and any expression alike of this. (Only works for this kind of binomial). 1) The first factor, which is a binomial, is always the cube root of the two terms. (The blank space represents the missing terms and its operation/ sign). a3 - b3 = (a -...

This is my solution:

I got this part: πr2 / 4 - r2/2 arcsin (cos θ) Can you show me how, please?

I know how to integrate constants. I just don't know how to simplify my solution to 1/2 r2 θ. We had study about polar coordinates and I know it, I just don't know how to make equations for the integration process.

I am finish in integrating it with values.. I am stuck on how the integration will cancel out to come up with only 1/2 r2 θ for the area. What do you mean by polar coordinates? I think I work with cartesian coordinates in integrating?

I have done it by means of basic integration of plane areas. I divide the figure into two parts as A1 and A2 for computing the area. It is somehow like this (I can't find a picture of my solution). I draw a triangle from A perpendicular to CB. Now, the sector is divided into a triangle and...

I am bothered on how the area of circular sector was derived using integration. I have a solution but I don't know how it will go and come up with the formula: A = 1/2 sr and A = 1/2 r2 θ Can someone show me the solution for...