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char808
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Homework Statement
indefinite integral 5[tex]\pi[/tex]cos[tex]\pi[/tex]t
Homework Equations
The Attempt at a Solution
5[tex]\pi[/tex] int cos[tex]\pi[/tex]t
Substitution Method
5[tex]\pi[/tex] x sin (1/[tex]\pi[/tex]t
Is this your integral?char808 said:Homework Statement
indefinite integral 5[tex]\pi[/tex]cos[tex]\pi[/tex]t
Homework Equations
The Attempt at a Solution
5[tex]\pi[/tex] int cos[tex]\pi[/tex]t
Substitution Method
5[tex]\pi[/tex] x sin (1/[tex]\pi[/tex]t
Integration by substitution is a technique used in calculus to find the indefinite integral of a function. It involves replacing a variable in the integrand with a new variable, and then using the chain rule to find the integral.
Integration by substitution is typically used when the integrand contains a composition of functions, such as f(g(x)). In these cases, substitution can help simplify the integral and make it easier to solve.
The general process for integration by substitution involves four steps: 1) Identify a composition of functions in the integrand, 2) Choose a new variable to replace the inner function, 3) Calculate the derivative of the new variable, and 4) Rewrite the integral in terms of the new variable and solve.
In theory, any function can be solved using integration by substitution. However, the effectiveness of this technique depends on the complexity of the integrand and the availability of an appropriate substitution. In some cases, other integration techniques may be more efficient.
One common mistake when using integration by substitution is forgetting to include the derivative of the new variable in the integral. This can lead to incorrect solutions. It is also important to choose a suitable substitution that simplifies the integral, rather than making it more complicated.