Help with Diff EQ Integrals Using Trig Substitution

In summary, a differential equation is a mathematical equation used to model physical phenomena. Trigonometric substitution is a method for simplifying integrals by replacing a variable with a trigonometric function. It is typically used in integrals with square root expressions or quadratic expressions that cannot be factored. The most commonly used trigonometric substitutions are sine, cosine, tangent, secant, and cosecant. The steps for solving an integral using trigonometric substitution include identifying the appropriate substitution, simplifying the integrand, using trigonometric identities, integrating with respect to the new variable, and converting the final answer back to the original variable.
  • #1
Weatherkid11
18
0
I am working on a Differential Equation problem and I am stuck on these two integrals: http://forums.cramster.com/Answer-Board/Image/cramster-equation-20064101738436328028752372062504976.gif and http://forums.cramster.com/Answer-Board/Image/cramster-equation-20064101739556328028759586125007822.gif I think i have to use trig substitution but not sure. Please help, this is only a step to the problem, i got the rest of it.
 
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  • #2
you can simplify both of them to make it easier
 
  • #3
csc(x)= 1/sin(x) should help.
 

Related to Help with Diff EQ Integrals Using Trig Substitution

What is a differential equation?

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It is used to model various physical phenomena in fields such as physics, engineering, and economics.

What is a trigonometric substitution?

A trigonometric substitution is a method used for simplifying integrals by replacing a variable with a trigonometric function. This allows for easier integration and evaluation of the integral.

How do I know when to use trigonometric substitution?

Trigonometric substitution is typically used when there is a square root expression, or an expression that contains a sum or difference of squares, in the integrand. It can also be used when the integrand contains a quadratic expression that cannot be factored.

What are the common trigonometric substitutions used in differential equations?

The most commonly used trigonometric substitutions are sine, cosine, tangent, secant, and cosecant. These functions can be used to replace a variable in the integral and simplify the expression.

What are the steps for solving an integral using trigonometric substitution?

The steps for solving an integral using trigonometric substitution are:

  1. Identify the appropriate substitution based on the form of the integral
  2. Make the substitution and simplify the integrand
  3. Use trigonometric identities to further simplify the expression
  4. Integrate the simplified expression with respect to the new variable
  5. Convert the final answer back to the original variable

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