devotion & mathematics

              DOUBLE INTEGRALS               The line integrals are often used to find the lengths of the curves i.e if we talk about a circle the line integral is the circumference of the circle or semi circle or quarter circle etc. If we ask about the length of the curve on the circle which is not a complete circle or semi or quarte circle , we chose the part of the circumference of the circle then we need some procedure or  theory to find the length of the curve which are called the line integrals.          This process of line integration is applicable not only for the circles but also for any one or two or three dimensional regular  and irregular shapes .        So what about the surface area of circular cake in a rounded plate or cool drink bottle looks like a cylinder  or football like a sphere etc. In mathematics there are certain formulae for the ab...

                                                  AREA OFSUBSETS OF R 2 Area of a Rectangle in R 2   :                             In R 2 , the rectangle is defined as the set {(x, y)/a≤ x ≤ b, c≤ y≤ d}.                                                    The area is (b-a)(d-c). Area of a bounded subset in  R 2   which is not a rectangle :                                               ...

  Scalene triangle : A triangle where all three sides are in different lengths and all three angles are different measures. Properties of scalene triangl e: 1.All 3 sides are different in length. 2.All 3 angles are different. 3.The sum of all three interior angles is 180 degrees. 4.There are no lines of symmetry. Area of scalene triangle : 1.If height and base are given, then Area  A=(1/2)xbxh 2.If the 3 sides are given , then Area   A=√(s (s-a)(s-b)(s-c) where s=(a+b+c)/2,where a,b,c are given         sides. 3.If two sides and angle is given, then Area   A=(1/2)absinθ, where θ is the given angle and a,b are the       sides. Construction : 1.Draw a line segment for the longest sides of the triangle. 2.Use a protractor to  measure the given angle at one side of the line. 3.Construct a ray that's close to the line. 4.Use a compass and ruler to measure another side of triangle. 5.Put the compass at one end of...