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kiz
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Homework Statement
Homework Equations
The Attempt at a Solution
After substituting:
Using
I'm stuck here:
I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.
kiz said:Homework Statement
Homework Equations
The Attempt at a Solution
After substituting:
Using
I'm stuck here:
I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.
Dick said:http://en.wikipedia.org/wiki/Tangent_half-angle_formula You seem to have turned a '2' into a 'z' in you dx derivation. And you would have to change the limits to 'z' limits instead of 'x' limits if you are going to stick with the variable z. Otherwise just find the indefinite integral in terms of z and change the function back to x.
Trigonometric substitution is a technique used in calculus to simplify integrals involving trigonometric functions. It involves substituting a trigonometric expression in place of a variable in order to simplify the integral and make it easier to solve.
Trigonometric substitution is used in Calculus 2 to solve integrals that involve expressions with trigonometric functions, specifically when dealing with square roots or rational powers. The substitution allows for the integral to be transformed into a simpler form, making it easier to solve.
The formula for using Z = tan(x/2) in trigonometric substitution is:
tan(x/2) = Z, which can be rewritten as x = 2arctan(Z) or x = 2tan-1(Z).
You should use Z = tan(x/2) in trigonometric substitution when the integral involves a square root of a quadratic expression, or when the integrand contains a rational function with a quadratic denominator. Additionally, you can also use this substitution when dealing with integrals that involve the trigonometric functions secant and tangent.
Using Z = tan(x/2) in trigonometric substitution has several advantages. It can simplify the integral, turning it into a more manageable form. Additionally, it can help solve integrals that would be difficult to solve using other methods. It also allows for the use of trigonometric identities to further simplify the integral. Finally, it can be used to solve a wide range of integrals involving trigonometric functions.