- #1
annie122
- 51
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how do i go about integrating
x*sqrt(1-x^4)??
i have no idea
x*sqrt(1-x^4)??
i have no idea
Yuuki said:how do i go about integrating
\(\displaystyle \int x \cdot \sqrt{1-x^4}dx\)
i have no idea
Yuuki said:u = sin(w) right?
thx!
A trigonometric substitution is a technique used in integration to transform an integral involving algebraic expressions into one involving trigonometric functions. This is useful for solving integrals that cannot be solved by other methods.
Trigonometric substitutions are most commonly used when dealing with square roots of quadratic expressions, or when the integrand contains certain trigonometric functions such as sine, cosine, or tangent.
The three main types of trigonometric substitutions are:
When making a trigonometric substitution, you need to identify which type of substitution to use based on the form of the integrand. Then, you need to choose an appropriate trigonometric function to replace the variable in the integrand. Finally, you need to manipulate the integral using trigonometric identities to simplify it into a form that can be easily integrated.
One tip for solving integrals with trigonometric substitutions is to always check the limits of integration. This may require you to use a trigonometric identity to rewrite the limits in terms of the new variable. Additionally, it is helpful to practice identifying which type of trigonometric substitution to use for different types of integrals.