Advanced Math Solutions – Integral Calculator, the basics

Integration is the inverse of differentiation.   Even though derivatives are fairly straight forward, integrals are not. Some integration problems require techniques such as substitution, integration by parts, trigonometric substitutions, or possibly more than one method.   We will walk you through slowly, starting with the basic integration rules:  the constant multiplication rule, the power rule, and the sum rule.

Some common functions you should get familiar with (we’ll show you more later):
\int a dx = ax + C
\int x dx = \frac{x^2}{2} + C

One more thing to remember, always add the constant of integration C.

Let’s start with the Power Rule: \int x^n dx = \frac{x^{n+1}}{n+1} + C,\quad n\ne-1
The power rule simply tells you to divide by n+1 (the power + 1) and increase the power by 1, it’s that simple.  Here’s an example of how it works (click here):

Let’s continue with the constant multiplication rule (click here):
\int af(x) dx = a\int f(x)dx

The constant multiplication rule simply tells to take out the constant

Moving on to the Sum Rule (click here):

Putting it all together (click here):

That wasn’t too bad.  If you’d like to take a pick at some more advanced integrals click here

Cheers,
Michal

High School Math Solutions – Derivative Calculator, the Basics

Differentiation is a method to calculate the rate of change (or the slope at a point on the graph); we will not differentiate using the definition which requires some tricky work with limits; but instead we will use derivative rules that are fairly easy to memorize. We’ll start with the basics:

Constant:  (c)’=0
Power rule:  (xⁿ)’=nx^(n-1)
Multiplication by constant:  (cf(x))’=c(f(x))’
Sum/difference rule:  (f±g)’=f’± g’

We are good to go.

Let’s start with an example, click here to see how it works

Here’s another example (click here):

Until next time,
Michal