Essence of calculus

Transcript

the area of this circle is pi or squared but how calculus has the answer let's say this circle has radius 2. we can try chopping up this circle in many ways best way is to slice the circle into many concentric Rings now take one ring which have inner radius R start straightening out this ring this new shape is rectangle whose length is circumference but the thickness depends upon how finely you chopped therefore the area of this fine rectangle is you can visualize each and every chop by fitting rectangles side by side in the radius axis each of these rectangles extends to a point where it just barely touches the graph 2 pi r now if size of Dr gets smaller and smaller and the number of rectangle increases then the portion under the graph becomes the triangle therefore the area of this triangle is the area of the circle