- Finding integrals is the reverse of the derivative.
- There are online derivative calculators and integration calculators that you can benefit from easily.
- Such online calculators can also prove vital and effective for the students to learn different sorts of concepts regarding math.
As a science student, I always had tough times doing mathematics, but Integrals and Derivatives were way more fun than doing any other calculus problems. So let’s make it easy and fun for you all out there thinking Integrals and Derivatives are hard to do.
Definition of Derivatives
The Derivative is a way to show the rate of change the amount at which a function is changing at one given point.
A derivative is often written by using dy over dx (difference in y divided by difference in x), d is not a variable hence cannot be canceled.
Can be expressed as:
In a much easier view, the derivative is a slope of the tangent as it shows the change in the function of a given point.
Definition of Integral:
An integral computes the area between a function and a coordinate axis.
Finding integrals is the reverse of the derivative.
Integrals can be used to find areas, volumes, central points and many other useful things.
Integrals can be used to find areas, volumes, central points, and many other useful things.
As integrals are the sum of area, the volume under the curve of slope hence can be written as
Area under curve =? = y = fx
The international symbol for integral is a unique “S.”
∫ fx (dx)
This symbol actually explains the basic idea of integration, i.e., sum of summing slices that implies under that curve.
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Relation between Derivatives and Integrals
Integration is the reversal of derivation and likewise.
Like the answer of derivative is the question of integral and likewise the question statement of integration is the answer of derivation.
∫ 2x dx = x^2 + C
Plus C is a constant here hence;
2x + 4= x^2, 2x + 6= x^2 and so on. The ‘C’ always remains constant and has zero value as a result.
So when we reverse the operation (to find integral) we only know 2x, but there could have been a constant value
So we just wrap up the equation by just adding +C at the end.
Student’s issues with Calculus:
Let’s come to the burning point; what are the problems which students faced while doing calculus.
Firstly just not make it a big deal, as mathematics isn’t everyone’s cup of tea and especially when it comes to doing calculus. We are here to help you, so don’t freak out, just chill. There are online derivative calculators and integration calculators that you can benefit from easily. Such online calculators can also prove vital and effective for the students to learn different sorts of concepts regarding math.
Here are some most common questions I’ve come to know from the students:
Why is calculus considered to be difficult?
In my opinion, calculus relates to infinity and limits both at a time and it’s no fun in finding infinities and measuring the limits within the same equations. Hence it comes out with a lot of confusing statements to rely on as the final result.
What calculus exactly is?
As there are many pieces of research present on search engines which provide much knowledge of what exactly calculus is!
In a nutshell, Calculus is the study of changes in function and sequences.
Three main points are:
- Limits: Behavior of functions and sequences when getting closer to a desired point.
- Derivatives: The rate of changes in a function at point (the slope of the graph).
- Integrals: Cumulative effect of a function (the area under the curve).
The relation of the above three points is probably the Fundamental Theorem of Calculus, developed by none other than Leibniz and Newton.
Now the last but not least common problem is:
How to get the accurate solution of a calculus question?
It is the first thing you need the most while doing calculus to be focused on the steps, followed by the statements you made. Be careful while writing out every step, not to skip any step and don’t be sloppy.
Double check your computations. Just go back and revise all the steps from the very first to the final one. This way, you’ll go through the mistakes and wrong steps you did while doing calculus, so you rewrote your mistake and got an accurate answer.