The main aim of Differential Calculus is in finding out the slopes of various equations. In simple terms, slope is the Tangent of the angle, which a line makes with x - axis. One can determine it in terms of coordinates, which is an application of easy calculus. If the x and y coordinates of two points of a line are given as (k1, l1) and (k2, l2) in that order then its Slope is
Slope, s = (l2 – l1) / (k2 – k1) = Δ l / Δ k,
Here, ‘Δ l’ is difference in y – coordinates and ‘Δ k’ is difference in corresponding x – coordinates.
Differentiation is defined as the method of computing the Slope. The outcome of these computations is termed as the derivative. The branch of mathematics that incorporates this theory is known as differential calculus. We generally symbolize the derivative by dy / dx or f'(x).
Integral calculus is a subdivision of calculus that is related to calculating areas under curves. Integration is defined as the method of calculating area. The resulting formula used to deduce the area is called the integral. The subdivision of mathematics that deals with these concepts is called integral calculus. It can be noted that Integration is reverse of differentiation. The symbol of integration is ‘∫’.