Integrals of Trigonometric Functions

In summary, an integral of a trigonometric function is a mathematical operation used to calculate the area under the curve of a trigonometric function. The common trigonometric functions used in integrals are sine, cosine, tangent, cotangent, secant, and cosecant. To solve integrals of trigonometric functions, various integration techniques such as substitution, integration by parts, or trigonometric identities can be used. These integrals have many applications in physics, engineering, and other fields, and are also related to derivatives through the Fundamental Theorem of Calculus.
  • #1
recon_ind
8
0
I have three problems that I'm having a hard time with. I'd appreciate any help with
any of the three problems.

[tex]\int((cos(x))^6)dx[/tex]

AND

[tex]\int(x^3 * sqrt(x^2 - 1)[/tex]

AND

Solve for y (separation of variables):
dy/dx = ((2y + 3)^2)/((4x + 5)^2)

THANKS soo much.
 
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  • #2
first one reduction formuls or integration by parts (integrate cos(x) differentiate cos(x)^5)
second one substitute x^2-1->w
third one just separate and integrate
 

Related to Integrals of Trigonometric Functions

What is an integral of a trigonometric function?

An integral of a trigonometric function is a mathematical operation that calculates the area under the curve of a trigonometric function. It is denoted by ∫(f(x)dx) and is used to find the total value of a function within a given range.

What are the common trigonometric functions used in integrals?

The common trigonometric functions used in integrals are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are used to describe the relationship between the sides and angles of a triangle.

How do you solve integrals of trigonometric functions?

To solve integrals of trigonometric functions, you can use various integration techniques such as substitution, integration by parts, or trigonometric identities. It is important to identify the appropriate technique for each integral problem.

What are the applications of integrals of trigonometric functions?

Integrals of trigonometric functions have many applications in physics, engineering, and other fields. They are used to calculate areas, volumes, and other physical quantities. They are also used in solving differential equations and in Fourier analysis.

What is the relationship between integrals of trigonometric functions and derivatives?

The relationship between integrals of trigonometric functions and derivatives is described by the Fundamental Theorem of Calculus. It states that the derivative of an integral is equal to the original function. In other words, integration is the inverse operation of differentiation.

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