Integral Calculator

More Calculators

Limit of Sum Calculator

by Alan Walker

Last Updated March 07, 2023

Introduction to Integral Calculator

Our Advanced Integral calculator is the most comprehensive integral solution on the web with which you can perform lots of integration operations. You have to enter function, variable, and bounds, and you're good to go.

An Integration calculator with steps allows you to learn the concepts of calculating integrals without spending too much time. You can evaluate the integral using an integral calculator with steps easily online.

Similarly, you can find a double integral calculator on this website. The double integral calculator shows you graphs, plots, steps, and visual representation, which helps you learn advanced concepts of double integration.

There are many other useful calculators you can use to get benefit. Similarly, you can determine the volume of a solid of revolution with washer method calculator and determine the cross sections of a solid of revolution with disc method calculator.

How to solve Integration?

To solve for a definite integral, you have to understand first that definite integrals have start and endpoints, also known as limits or intervals, represented as (a,b) and are placed on top and bottom of the integral.

We can generalize integrals based on functions and domains through which integration is done. Integration by parts calculator with steps helps you to evaluate the integrals digitally.

For instance, a line integral is expressed with functions of two or more variables with the integration interval replaced with a curve connecting the two points on the interval.

On the other hand, there's a surface integral, where a character replaces the curve in 3-dimensional space.

The formula for integral (definite) goes like this:

$$\int_b^a f(x)dx$$

Where,

∫ represents integral

dx represents the differential of the 'x' variable

fx represents the integrand

point a and b represent limits of integration

Let's solve it considering that we're being asked for integral from 1 to 3, of 3x dx

$$\int_3^1 3(x)dx$$

Solving:

$$\int_b^a f(x)dx=-\int_b^a f(x)dx$$

$$-\int_3^1 3(x)dx$$

Take out the constant:

$$\int a.f(x)dx = a.\int f(x)dx$$

Applying the power rule:

$$\int x^a dx = x^a+1/a+1, a≠1$$

$$=-3[\frac{x^{1+1}}{1+1}]_1^3$$

simplify

$$-3[\frac{x^2}{2}]_1^3$$

calculating the boundaries: 4

-3.4

-12

On the other hand, the Indefinite integral is distinguished from the definite integral because of the former’s lack of defined limits.

Indefinite Integral thus goes by the formula:

$$\int f(x)dx$$

The above integration solver can calculate indefinite integral and definite integral, but if you want to calculate indefinite integral only, find the best online indefinite integral calculator.

Related: Find this useful blog to learn about definite integral and indefinite integral

How to calculate improper Integral?

One of the reasons why a definite integral becomes an improper integral is when one or both of the limits reach infinity. An Integral calculus calculator can be used to calculate improper integrals.

This integral is then solved by turning it into a problem of limits where c happens to approach infinity or negative infinity.

Let's consider an example where one of the limits of integration is infinite and then solve it.

$$\int_1^\infty \frac{1}{x^2} dx \;and\; \int_1^\infty \frac{1}{x} dx$$

$$\int_1^\infty \frac{1}{x^2} dx = \lim_{c\to \infty} \int_1^c \frac{1}{x^2} dx$$

$$\lim_{c\to \infty} [-\frac{1}{x}]_1^c$$

$$\lim_{c\to \infty} [-\frac {1}{c}] -(-\frac{1}{1})]$$

0+1

1

Since the answer to the improper integral is finite, we consider it converged.

If you only want to evaluate definite integrals, use this best step by step definite integral calculator online.

Related: Use shell method calculator with steps to find the volume of a solid of revolution easily online.

How to calculate Continuous Integration?

The fundamental theorem of calculus establishes a clear association between integral and differential calculus. Our integral calculator with steps is capable enough to calculate continuous integration.

If f(x) is continuous for the interval a and b given the variable x and G(x) is a function in such sense that dG/dx = f(x) for all values of x in (a,b)

Let f be continuous on an interval ‘y’. Select a point p in y then the function f(x) is defined as:

Let F(x) be as follows

$$\int_p^x f(t) dt$$

Let c be in i and let x be infinitely close to c and the endpoints of i. Then by addition,

$$\int_p^c f(t) dt = \int_p^x f(t) dt + \int_x^c f(t)dt$$

$$\int_p^c f(t) dt - \int_p^x f(t) dt + \int_x^c f(t)dt$$

$$f(c) - F(x)= \int_x^c f(t)dt$$

For your ease and advance learning regarding multiple integrals, we offer one of the quickest triple integral calculator. This tool will surely assist you in calculating definite and indefinite triple integrals online by doing few clicks.

What is Integral calculator?

For years there was only one way to evaluate the integrals, and that was through manual calculations. These days we have a lot of online integration calculators to calculate integration value easily. Most students usually have robust theoretical concepts of calculus. So evaluating the integrals or derivatives is not really a problem when we have calculators like integration calculator or derivative calculator.

However, it's a problem when it comes to home assignments when students usually get tons of issues requiring them to solve for integrals. For help, please read the article stating the integration, its importance and different methods.

Now, it wouldn't be smart to calculate integrals repeatedly by hand. This definite integral calculator comes in handy to compute complicated integration problems. It's free and simple to use and gets the answer almost instantaneously as you can find an integral calculator with steps easily online.

Also, use other useful math calculators, which are important in overall integration processes. Like laplace transform calculator helps you transform the integral of the given derivative function, and the fourier transform calculator enables you to change a function of time into frequency.

How to find the best integration calculator?

There are many integral calculators available on the web like calculatored, symbolab, wolframalpha and others.

However, our integral volume calculator is better, quicker, provides more functionality and is the best integration calculator with steps available on the web. Find out the benefits of using our online integral calculator.

When you put in the function, variable, upper and lower bounds of limits, our integral solver calculates the integral and displays all the steps involved to give the user a better understanding of calculating integration.

You can also calculate vertical integration and horizontal integration within the area of curves with our online integral calculator with limits.

That's not all. Our integral solver also displays anti-derivative calculations to users who might be interested in the mathematical concept and steps involved in integration.

Moreover, this integration by parts calculator comes with a visualization of the calculation through intuitive graphs.

How to use the Integral calculator with steps?

Using the integration by parts calculator is easy and fast.

Step 1: Enter the function

To evaluate the integrals, you must have a proper function. You need to enter your function in the function bar of the integration calculator. There is also a "load example" list. You can click that list to load an example equation for calculating integrals step by step.

Step 2: Select the Variable

For evaluating integrals, there are three variables you can use. These variables are x, y and z. The role of these three variables differs from each other, and all 3 have different impacts on the overall output. You can select the variables as x, y and z from the variable section.

Step 3: Give Upper bound value

The upper bound is the value that helps us sum integral at its maximum value. The upper bound is denoted as U, and its determination is crucial in the integration process. You can enter the upper bound of your limit in the upper bound section of the upper bound calculator.

Step 4: Give Lower bound value

The lower bound is the smallest value that we set to start the integration. To get the accurate integration results, the smallest value of an interval is denoted by L. To get the precise integration results. You need to enter the actual amount of your lower bound limit in the lower bound section of the upper and lower bounds calculator.

After completing all above steps Press "GO" button.

Immediately after clicking the button our integral calculus calculator will start working. The integration by parts calculator will show you the anti derivative, integral steps, parsing tree and plot of your result. All these functionalities and features makes this the best line integral calculator to evaluate the integral of complicated integration problems.

As you're going through the process of inputs, a visual equation would be displayed below the inputs where you can visualize how your inputs would look like in Equation.

FAQ's

How to Evaluate Integrals?

There are two types of integrals, definite and indefinite integrals. You can solve them both by integration. The difference is that you need to put the limit values after integration in definite integrals, whereas in indefinite integrals, you don’t need to put limit values.

Integrals calculator helps to solve out every type of definite and indefinite problems easily.

What is the integral of ex?

The integral of ex is:

$$\int e^x dx \;=\; \frac{e^x}{1}+c$$ $$\int e^x dx \;=\; e^x+c$$

The integration of exponential functions is tricky, but we provide great tools to evaluate integral online.

How to Evaluate the Integral by Interpreting it in terms of Areas?

Solving integration online are basically finding the area under a specific curve. For example of a given equation of curve 1-x with upper and lower bound x=-4 and x=3, the area will be calculated as,

$$\int_{-4}^3 (1-x) dx \;=\; \Biggr| x - \frac{x^2}{2} \Biggr|_{-4}^3$$ $$\int_{-4}^3 (1-x) dx \;=\; \left( 3 - \frac{3^2}{2} \right) \;-\; \left( -4 - \frac{(-4)^2}{2} \right)$$ $$\int_{-4}^3 (1-x) dx \;=\; \left( 3 - \frac{9}{2} \right) \;-\; \left( -4 -2 \right) \;=\; \frac{21}{2}$$

So the area under the given curve is 21/2. We can verify this by evaluate the integral calculator for cross-checking your answer.

The calculator integral is the great resource for this type of calculations to save your time.

What is the integral of 1/x?

The integral of 1/x is,

$$\int \frac{1}{x} dx \;=\; ln(x) + c$$

Have a fun calculating integrals with integral online calculator!

Other online integration calculators

There are a lot of other step by step integral calculators on this website which you can use for free. These tools are: