### Calculus Apps

The educators at Vedantu explain the key concepts in a way the students can easily grasp it well enough to solve complex sums. The educators use creative 3D graphics, short animated educational videos for better and effective learning.

Nowadays, apps have been introduced to solve advanced problems of calculus with maximum accuracy. The apps can easily be installed in the Google play store.

With the advent of technology, solving complex mathematical equations has become a matter of seconds. These math problems solving apps can help solve anything from basic problems to the most complex problems. The apps also provide a step-by-step process of how it solved the answer.

In some of these apps, you can simply click a picture of that equation and the app will provide you with the answer in the most accurate way.

### Uses of Calculus Apps

Limit of a function

Differentiation

Integration (Definite and indefinite)

Maxima and minima

Approximate area of circles with the use of rectangles.

Taylor polynomial

One can easily find some of the best apps for Calculus on Google Play Store and iOS Apps Store.

### Calculus Explained

Integration is defined as the summation of all discrete elements. Integration is used to find volume, displacement and, the area which cannot be measured otherwise since it's very small.

Basically, it is exactly the opposite of differentiation.

There are two types of integration:

Differential Calculus

Integral Calculus

Integral Calculus can be two types that are Indefinite integral and definite integral.

Integration is used to find the antiderivative of a function whereas as we already know differentiation helps in finding the derivative of a function.

Therefore, it is exactly the opposite of the way differentiation is solved.

For example: for a function f(x) = sin x

The differentiation of f(x):

d f(x)/ dx = cos x

To find the antiderivative of a function ∫, this is introduced.

Therefore, it can be shown as:

∫f (x) dx= F(x) + c

Here, f(x) is called the integrand of the function, and c is the constant.

### Indefinite Integration

Integration without the use of limits.

It is represented as follows:

∫(2x²-3x)dx

### Definite Integral

Integration with the use of lower and upper limits is called a definite integral.

For example:

\[\int_{a}^{b}\] (2x²- 3x)

Some basic formulae one must know in order to solve integration:

∫ dx = x + C.

∫ a dx = ax + C.

∫ xn dx = ((xn+1)/(n+1))+C ; n≠1.

∫ sin x dx = – cos x + C.

∫ cos x dx = sin x + C.

∫ sec2 dx = tan x + C.

∫ cosec2 dx = -cot x + C.

∫ sec x (tan x) dx = sec x + C.

∫ (1/x) dx = ln |x| + C

∫ ex dx = ex+ C∫ ax dx = (ax/ln a) + C ; a>0, a≠1

Example:

∫ 2x² + 3x + 7

Solution:

∫(2x² + 3x + 7)dx

= 2 ∫1x² dx + 3 ∫ x dx + ∫7 dx

= 2 x³/3 + 3x² /3 + 7x

## Applications of Calculus

### Software Developer:

They may use these apps to determine and meet a user's software needs or for preparing models for programmers.

### Economist:

An economist studies and analyses several economic issues using advanced mathematics. These apps can also help the economist for research purposes.

### Aerospace Engineer:

An aerospace engineer uses advanced mathematical tools to develop or build different aerospace products, like satellites, missiles, spacecraft, aircraft.

### Chemists:

In the field of chemistry, calculus is used to determine the rate of change in a chemical equation.

1. How Do Most of these Calculus-based Apps Function?

Ans: Most of these apps use advanced AI technology to solve complex problems with great ease. The apps are quite simple to use. In some of these apps, you just need to click a photo of the equation and the app will show you the stepwise result whereas some apps provide a built-in calculator where you can enter an equation.

The apps will identify the problems instantly and deliver us the most accurate result. Many of these apps not only solve the equation but also provide you with similar problems, interactive graphs, and video lectures from the internet.

2. Are All these Apps Free of Cost?

Ans: Yes, all these apps can be used for free on Android. The free version of most of these apps will provide only the answers whereas the monthly or yearly subscription will give you stepwise solutions to math problems with a wide array of math types.

If you are a daily user, then it is highly suggested that you get a subscription to these apps. These apps are very convenient to use. It is designed in a way that it would produce the most accurate answers with the minimum amount of errors.

3. Should I Learn Calculus from Vedantu?

Ans: Calculus is a very crucial topic in Mathematics. This chapter forms the foundation of many subjects in higher studies. So, a student must grasp the concepts well enough to solve complex problems. The regular classes offered by Vedantu helps the students build an in-depth understanding of the key concepts of Calculus.

The study material and the solutions are prepared as per the CBSE guidelines. The solutions are prepared by the top educators who have gained expertise in this field over the years. Vedantu gives its students the utmost priority and helps them in all possible ways to achieve their goals. Vedantu is one of the most reliable and trustworthy online coaching institutes in India.