Can substitution be used to solve these trigonometric integrals?

In summary, the two problems discussed are the integral of (sec^3x)(tan x)dx and the integral of (sec^4x)(tan x)dx. The question of whether substitution will work for both of these problems is raised, and it is suggested to try substitution to see if it works. The person responding has tried substitution and obtained an answer for both problems, but believes that following the rule of changing sec^4x to (tan+1)(sec^2x) may be necessary. However, changing the sec^2x does not result in the same answer. A suggested substitution is to replace tan(x) by sin(x)/cos(x), keeping in mind that sec(x) = 1/cos
  • #1
Steel_City82
14
0
the two problems are
the integral of (sec^3x)(tan x)dx
and the integral of (sec^4x)(tan x)dx

will substitution work for both of these problems
 
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  • #2
Why don't you just try substitution and see if it works?
 
  • #3
I did and I got an answer for both, but for some reason I think I should follow the rule and change the sec^4x to (tan+1)(sec^2x)

and you don't get the same answer when you do it like that

if you just strait substitute you get sec^7x/5
and if you change a sec^2x to 1+tan you get tan^4x/2
I think, that's if I am even doing it right
 
  • #4
Replace tan(x) by sin(x)/cos(x) (bearing in mind that sec(x) = 1/cos(x)) and the substitution should be clear :smile:
 

FAQ: Can substitution be used to solve these trigonometric integrals?

What are trigonometric integrals?

Trigonometric integrals are integrals (or antiderivatives) of trigonometric functions such as sine, cosine, tangent, etc. These integrals are important in mathematics and physics for solving various problems involving periodic functions.

How do you solve trigonometric integrals?

To solve trigonometric integrals, we use various techniques such as substitution, integration by parts, trigonometric identities, and special formulas. The method used depends on the form of the integral and may require some algebraic manipulation.

What are the most common trigonometric integrals?

The most common trigonometric integrals include integrals of sine, cosine, tangent, secant, cosecant, and their inverse functions. These integrals are used in many applications, including physics, engineering, and geometry.

Are there any tricks for solving trigonometric integrals?

Yes, there are some useful tricks that can help in solving trigonometric integrals. These include using trigonometric identities, converting trigonometric functions to their equivalent forms, and using symmetry properties of trigonometric functions.

Why are trigonometric integrals important?

Trigonometric integrals play a crucial role in mathematics and its applications. They are used to solve various problems in physics, engineering, and other fields that involve periodic functions. These integrals also help in finding areas, volumes, and other important quantities in calculus.

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