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vande060
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Homework Statement
S cos^5x/sin^1/2x
Homework Equations
The Attempt at a Solution
S cos^5x/sin^1/2x
t = sin^1/2x
t^2 = sinx
2t dt = cosx dx
substituting back in
S 2tcos^4x/t
S 2cos^4x
Last edited:
Dick said:Try substituting just t=sin(x).
Yes, substitution is a commonly used technique to simplify integrals. It involves replacing a variable with a new one in order to make the integral easier to solve.
Yes, there are various techniques for simplifying integrals, such as integration by parts, trigonometric substitution, and partial fraction decomposition. It is important to choose the most appropriate method based on the form of the integral.
Yes, sometimes splitting an integral into smaller parts can make it more manageable. This is particularly useful for integrals involving piecewise functions or functions with multiple terms.
Yes, some functions are easier to integrate than others. Generally, polynomials, exponential functions, and trigonometric functions are simpler to integrate compared to rational functions or functions involving radicals.
If the limits of integration for an integral are -a to a, the function being integrated is even. If the limits are -a to a, the function is odd. Alternatively, you can check if the integrand is unchanged when x is replaced with -x (even) or -x (odd).