Trigonometric Substitution Calculator

Result:

Please wait.. loading-icon

More Calculators

Trigonometric Substitution Calculator With Steps - An Introduction

The trigonometric substitution integral calculator is a freely available tool for substituting trigonometric functions. It is used to identify different integrals with radical expressions. Then simplify them using the various trigonometric functions.

Moreover, If you're looking for another useful integration technique, you might want to try our U Subs Calculator. It can help you integrate a wide variety of functions using the technique of u-substitution.

What is Trig Substitution Calculator with steps?

The trig sub integral calculator is a free online tool for substituting radical expression in trigonometric functions. These trigonometric functions makes it very convenient to do calculations. This trigonometric integral calculator make it easier to do this type of calculation. The tool is error-free and gives accurate results in a fraction of a second.

trigonometric substitution calculator with steps

So, if you're dealing with an integral that involves expressions like sin(x), cos(x), or tan(x), you might want to try our trig sub calculator with steps. It can help you simplify these expressions and make them easier to integrate using the powerful technique of trigonometric substitution.

How to Solve Integrals By Trigonometric Substitution?

To solve integrals by trigonometric substitution, you have to understand first that trigonometric substitution is a complex method in integration. This substitution method of integration replaces complex integral to trigonometric function for making its calculation easy.

So following are some formulas that we replace with corresponding trigonometric functions.

$$ \text{For} \sqrt{a^2-x^2}, \;\; \text{substitue} x \;=\; a sinθ $$ $$ \text{For} \sqrt{a^2+x^2}, \;\; \text{substitue} x \;=\; a tanθ $$ $$ \text{For} \sqrt{x^2-a^2}, \;\; \text{substitue} x \;=\; a secθ $$

Solving integration by substituion using integral calculator trig sub is quite easy. But let's understand how to substitue integral by trig substituion method with an example. This will help to lear the calculation of this type of integrand.

Example: Calculate the following integral:

$$ \int \frac{dx}{a^2+x^2} $$

Solution: We may write

x = a tanθ , dx = a sec2θ dθ , θ = tan-1(x/a)

$$ \int \frac{dx}{a^2+x^2} \;=\; \int \frac{a sec^2θ dθ}{a^2+a^2tan^2θ} $$ $$ =\; \int \frac{a sec^2θ dθ}{a^2(1+tan^2θ)} $$ $$ =\; \int \frac{a sec^2θ dθ}{a^2 sec^2θ} $$ $$ =\; \int \frac{dθ}{a} $$ $$ =\; \frac{θ}{a} $$ $$ ⇒\; \frac{1}{a} tan^{-1}{x}{a} + C $$

So, In this way we have proved that how to substitute complex rational intergrand in terms of trigonometric substitution.

If you're dealing with a product of functions that's difficult to integrate, you might want to try integration by parts. Our integration by parts calculator with steps can help you integrate these types of functions using this powerful technique.

How does Trigonometric Substitution Integral Calculator Work?

The following steps are used by the trigonometric substitution integral calculator with steps, are as follows:

Step 1: Firstly, enter the value of the base and perpendicular sides of the corresponding figure in the required input fields.

Step 2: Now click on the button “Calculate” to get the trigonometric integral functions.

Step 3: Finally, the value of the six trigonometric functions and the output field on your device screen is displayed.

Another powerful integration technique is integration by partial fractions. Our partial fraction integral calculator can help you break down complex rational functions into simpler fractions that are easier to integrate.

How to Find Trig Sub Integral Calculator?

The following steps are followed to find this online calculator:

  1. First of all, enter the keywords in the search bar.
  2. Google shows you some suggestions for the searched calculators.
  3. Now select the integration calculator with steps from Google suggestions.
  4. Then choose the calculator for the trigonometric integral calculator displayed on your screen.

Benefits of Trigonometric Integral Calculator

The trig substitution integrals calculator has the following benefits in solving the trigonometric integral functions:

  • The trigonometric substitution integral calculator will calculate the problems in just a few minutes and solve the different trigonometric functions step-by-step.
  • It is a time-saving tool for solving the integral in long divisions.
  • It keeps you away from complex and hectic manual calculations for complex trigonometric functions.
  • This trig sub calculator with steps determines the complex integrals using the substitution method of trigonometric functions.
  • The trig substitution calculator with steps evaluates the area of different trigonometric functions.
  • This trigonometric integral calculator is used to simplify the integrals containing the radical expressions.
  • The results of this tool are reliable and 100% accurate.
  • The trig substitution integrals calculator gives you accurate and authentic results.
  • This trigonometric substitution calculator with steps tool is faster and easier.
  • This calculator is easy to use and keeps you away from manual calculations.

So we hope you like our efforts on this trig substitution calculator with steps. Must try our new tools like area under a curve calculator. Don't be hesitate to share your reviews to us. So that we may improve ourself according to modern learnings.

Frequently Asked Question

What is the purpose of using a trigonometric substitution?

In mathematics, trigonometric substitution is substituting the trigonometric functions for other radical expressions. In calculus, trigonometric substitution is a way of calculating the integrals. Moreover, we may use trigonometric identities to simplify certain integrals containing radical expressions.

When can we use trigonometric substitution?

The Trig substitution method is suitable when we have an integrand containing the sum or difference of the squares of a constant and a variable, i.e., one of the forms x2+a2, a2−x2, and x2−a2.

When to use u-substitution vs trig substitution?

Generally, trig substitution is used for integrals of form x2±a2 or √x2±a2, while the u-substitution is used when a function and its derivative appear in the form of integrals.