# Trigonometric Substitution Calculator

## More Calculators ### Integral Calculator ### Double Integral Calculator ### Triple Integral Calculator ### Definite Integral Calculator ### Indefinite Integral Calculator ### Shell Method Calculator ### Washer Method Calculator ### Disc Method Calculator ### Laplace Transform Calculator ### Fourier Transform Calculator ### Improper Integral Calculator ### Integration by Partial Fractions Calculator ### U Substitution Calculator ### Trigonometric Substitution Calculator ### Integration by parts calculator ### Long Division Calculator ### Area Under the curve calculator ### Riemann Sum Calculator ### Trapezoidal Rule Calculator ### Area between Curves Calculator ### Simpson's Rule Calculator ### Arc Length Calculator ### Arc Length of Polar Curve Calculator ### Limit of Sum Calculator ##### by Alan Walker

Last Updated August 17, 2022

## Introduction to Trigonometric Substitution Calculator

The trig substitution calculator is an advanced online tool which helps in finding or evaluating the integrals functions. The trigonometric substitution refers to the substitution of trigonometric functions for other expressions. The trigonometric substitution method calculator is used to identify the definite and indefnite integrals that consist of radical expressions.

The integration by trigonometric substitution calculator will ease you in solving the trigonometric substitution. Otherwise it is considered the most difficult function in manual solution. The trigonometric substitution is a long and difficult process which can be sorted out in just a few seconds with the help of a trig substitution calculator.

Also try u substitution calculator, for evaluating other types of substitution in integration.

## How to find a Trigonometric Substitution Integral Calculator with steps?

In a world full of technology it is more easy to search anything on the internet. The trigonometric calculator is one of the most advanced tools available online. You can also find trigonometric integral calculator to get step by step answer.

The simple steps for finding this online tool is:

1. The best source for searching trig substitution calculator online is Google. You can use the main keyword of the online calculator that is “Trigonometric Substitution Calculator with steps”. Google will direct you to the various online calculators that provide the service to find the trigonometric substitution. It is all up to you to choose the right calculator for your function and wisely choose which is best for you.
2. When google shows you the multiple online tools for trigonometric substitution then carefully understand the instructions of the online calculator and its uses.
3. Another step of finding the trigonometric substitution integration calculator is to write the website name of “Calculator Integral” which has different online tools related to integrals. The integral calculator has a variety of calculators from which you can find the online calculator for trigonometric substitution.

To calculate integration by parts and by partial fractions use integration by parts calculator & partial fractions integration calculator for free easily.

## Benefits of using Trig Sub Calculator with steps

There are a lot of benefits of using the trigonometric substitution integral calculator. The trigonometric substitution is simple and easy to use. The substitution method calculator will help you in solving the functions step by step. Some of the benefits of using the integration by trigonometric substitution calculator are:

1. The trigonometric calculator helps in calculating the integrals of the trigonometric substitution function in a few seconds and step you away from manual calculation.
2. The integration by trigonometric substitution calculator will help in saving the time. It gives the answer of any equation in a few seconds.
3. You can do practice to consolidate your concepts related to trigonometric substitution.
4. It provides plot and possible intermediate steps of trigonometric functions.
5. It provides real part, imaginary part & alternate form of the integral within the results.

Related: Calculate integrals through improper integral methods easily by using our improper integrals calculator and also find area under a curve calculator respectively.

## Results provided by Integral Calculator Trigonometric Substitution

The conclusion or the results that are acquired by the trigonometric integrals calculator are very accurate and quick. The trigonometric substitution method calculator will give the authentic result and give the result step by step that will be easy to understand. The results obtained from the trigonometric substitution integration calculator are definitive.

You can find the real part, imaginary part, intermediate steps, alternate form of the integral and series expansion of the integral within results.

We also provide some unique calculator such as volume by shells calculator to complete your need to find the volume of solid of revolution.

## Is Trigonometric Integral Calculator reliable?

The trigonometric substitution calculator is very reliable as it helps in evaluating trigonometric functions step by step. The results which are obtained from using this tool are considered as accurate. The substitution method calculator helps in saving time and increases your chances of learning more efficiently.

Related: Also find double riemann sum calculator or trapezoidal calculator for evaluating area under the curve online.

## How to use a Trig Substitution Calculator with steps?

The integral calculator trigonometric substitution is easy to use. It has simple steps which you can be understood easily. Some of these steps is as follows:

1. To operate the substitution method calculator, the first step is to select the function if available or enter the function on the calculator.
2. Select whether you want to evaluate trigonometric functions as per definite integral or indefinite integral.
3. If you selected definite integral, then select the upper bound and lower bound for the process of integration on the calculator.
4. Select the variables with respect to x, y, z.
5. Click on the “Calculate” button. The integration using trigonometric substitution calculator will calculate the total function in a few seconds and give you the solution step by step.

No doubt trigonometric substitution calculator also provides the long and complex integration of function. But for solution of improper fraction you may try our long division integration calculator.

## Why to use Integration by Trigonometric Substitution Calculator?

Trig substitution calculator is very helpful in evaluating the functions or integrals. The substitution method calculator has different purposes of operating as it saves the time and energy in solving the trigonometric functions.

The calculator provides step by step results that will help in understanding the trigonometric substitution fully. The integration using trig substitution calculator is free of cost and also has simple instructions for use of integral calculator which can easily be followed or helps in solving the function either in definite integrals or indefinite integrals.

### What is trigonometric substitution in calculus?

In calculus, the trigonometric substitution is a method of substitution in the integrals to solve them. This substitution method involves the substitution of trigonometric functions in the original function.

This technique helps to solve complex integrals. You can also use integral trigonometric substitution calculator to get desired results online.

### Why do we use trigonometric substitution?

The trigonometric substitution is used when you don’t have a perfect square root of the function. When the function becomes unable to integrate, the substitution method helps to solve it by the substitution of trigonometric functions. Use trig substitution integral calculator to get instant results with plot and graph.

## How do you integrate using trigonometric substitution?

Suppose an integral of the form ∫dx / √(a^2 - x^2 ) , we can use trigonometric substitution method to solve it.

We may substitute,

$$x\;=\;a\;sin⁡θ \;\;,\;\;dx\;=\;a\;cos⁡θ dθ\;\;,\;\;θ\;=\;sin^{-1}\frac{x}{a}$$

Then

$$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;∫\;\frac{a\;cos⁡θ\;dθ}{\sqrt{a^2\;-\;a^2 sinθ^2}}$$ $$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;∫\;\frac{a\;cos⁡θ\;dθ}{\sqrt{a^2(1\;-\;sin^2\;θ)}}$$ $$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;∫\;\frac{a\;cos⁡θ\;dθ}{\sqrt{a^2(cos^2\;θ)}}$$ $$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;∫\;\frac{a\;cos⁡θ\;dθ}{a\;cos⁡θ}\;=\;∫\;1d\;θ$$

So,

$$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;θ\;+\;C$$

Now substituting the value of θ

$$∫\frac{dx}{\sqrt{a^2\;-\;x^2}}\;=\;sin^{-1}\;\frac{x}{a}\;+\;C$$

### Are trig functions polynomials?

No, the trigonometric functions are not polynomials. Even if these function involves variables, there can’t be known as polynomials. Polynomial functions also doesn’t involve trigonometric functions. You can use integration of trigonometric functions calculator if you want to solve them online.

### Are trig functions differentiable?

Yes, you can differentiate trig functions by using the definition of derivatives. There are also many theorems based on the differentiation of trig function for example, the function sin x is differentiable everywhere. With trig integral calculator, you can calculate trig functions free online.

### What trig functions are undefined?

The trig functions can be undefined on different case of angle values. For example if x=0 for sin x, the function becomes zero. Or if we take x=0 for cosecx, which is the reciprocal of sin x. gives the undefined value as the denominator is zero.

• Kauan Henrique
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