Calculus is a branch of Mathematics which contains formulas and methods to find lengths, areas, volumes etc. of 2-D and 3-D shapes by using techniques of Differentiation and Integration. Calculus consists of two sub-branches which are Differential Calculus and Integral Calculus. Calculus calculator is a great online tool which can quickly find the solutions to the calculus questions.
Example 1: Find the derivative of the function, f(x) = x3 + x2
To find the derivative, the Power rule of the Derivatives says that:
d(xn)/dx = n * xn-1
We can distribute the derivative to both the terms:
d(x3 + x2)/dx [ d(x3)/dx ] + [ d(x2)/dx ]
Using the above formula, we get
(3 * x3-1) + (2 * x2-1)
(3 * x2) + (2 * x1)
3x2 + 2x
Example 2: Find the integral of the function, f(x) = 3x2 + 2x
The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c
where ‘c’ is a constant
We can distribute the integral sign to both terms:
∫(3x2 + 2x) = ∫3x2 dx + ∫2x dx
Using the above formula, we get
3 * x2+1/ (2+1) + 2 * x1+1/ (1+1) + c
3 * x3/ 3 + 2 * x2/ 2 + c
x3 + x2 + c