Table of Contents

## How do you differentiate and integrate?

The differentiation of a function f(x) gives f'(x) which is the derivative of f(x), and further the integration of f'(x) gives back the original function f(x)….Differentiation and Integration Formulas.

Differentiation | Integration |
---|---|

d(ex)/dx = ex | ∫ex dx = ex + C |

d(ax)/dx = ax log a | ∫ax dx = ax/log a + C |

d(ln x)/dx = 1/x | ∫(1/x) dx = ln x + C |

### How do you explain calculus?

- Calculus is a branch of mathematics that describes continuous change.
- Differential calculus is used to find the rate of change of a variable—compared to another variable.
- Integral calculus is the process of calculating the area underneath a graph of a function.

**Is it possible to find the integral of 2x?**

… finding an Integral is the reverse of finding a Derivative. (So you should really know about Derivatives before reading more!) An integral of 2x is x 2 (More about “+C” later.) Integration can sometimes be that easy!

**How do you find the integral of a function?**

The symbol for “Integral” is a stylish “S”. (for “Sum”, the idea of summing slices): After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width). And here is how we write the answer:

## How do you find the integral of an improper rational function?

Any improper rational function can be decomposed into the sum of a polynomial plus a proper rational function. Therefore, the integral of an improper rational function can be written: To solve the integral of a rational function is decomposed into a sum of simple fractions: 1) The denominator is decomposed into a product of factors as follows:

### Can this integral be done with only the first two terms?

This integral can’t be done. There is division by zero in the third term at t = 0 t = 0 and t = 0 t = 0 lies in the interval of integration. The fact that the first two terms can be integrated doesn’t matter. If even one term in the integral can’t be integrated then the whole integral can’t be done.