Antiderivative Graph: Complete Explanation and Examples

The antiderivative graph is the graph of the antiderivative or integral of a given function. Take note that if we take the antiderivative of a derivative, it will provide us with the original function. Hence, when we want to sketch or draw the graph of an antiderivative, we are converting a derivative function to its […]

Rolle’s Theorem – Explanation and Examples

Rolle’s theorem states that if a real-valued function is continuous in a closed interval $[a,b]$ and is differentiable on the open interval $(a,b)$ while $f(a) = f(b)$, then there must be a point “$c$” in the open interval $(a,b)$ such that $f'(c) = 0$. The graphical representation of Rolle’s theorem is given below. Read moreFunction […]

Evaluating the Integral of 1/x

The process of integration is considered the reverse of taking the derivative of a function. We can look at integrals in such a way that the function being integrated is the function in its derivative form while the integral of that function is the original function. That is: begin{align*} int f(x)=F(x)+C end{align*} where begin{align*} dfrac{d}{dx} […]

Complex Derivative: Detailed Explanation and Examples

A complex derivative is a derivative that tells us about the rate of change of a complex function. A complex function has two parts, one is a real component and the other is an imaginary component. Complex functions are mathematically represented as: $f(z) = u (x,y) + i v (x,y)$ Read moreFunction Operations – Explanation and […]

Integral of x^1.x^2: A Complete Guide

The integral of $x^{1}.x^{2}$ is basically the integration of $x^{3}$ and the integral of $x^{3}$ is $dfrac{x^{4}}{4} + c$, where the “c” is a constant. The integral of $x^{3}$ is mathematically written as $int x^{3}$. Integration is basically taking the antiderivative of a function, so in this case, we are taking the antiderivative of $x^{3}$. […]