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DigiDigi
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How do I integrate sqrt(x/2-x)dx?
HS-Scientist said:I'm assuming it is the later. [itex] \int \sqrt{\frac{x}{2-x}} dx= \int \frac{\sqrt{x}}{\sqrt{2-x}} dx[/itex]
Use the substitution [itex] u= \sqrt{2-x} [/itex] to turn the integral into [itex] -2 \int \sqrt{2-u^2} du [/itex], which you can do by trig substitution.
The formula for integrating sqrt(x/2-x) is:
∫ sqrt(x/2-x) dx = (2/3) * (x - 2) * sqrt(2x - x^2) + C
To solve the integral of sqrt(x/2-x), you can use the substitution method. Let u = 2x - x^2, then du = (2 - 2x) dx. After substituting u and du into the integral, you can simplify the expression and use basic integration rules to solve for the integral.
Yes, you can use integration by parts to solve sqrt(x/2-x)dx. However, it may be more complicated and time-consuming compared to using the substitution method.
Yes, there is a specific range of values for x when integrating sqrt(x/2-x). The function is only defined for x values between 0 and 2. Any values outside of this range will result in an undefined integral.
Yes, you can use a calculator to solve the integral of sqrt(x/2-x). Most scientific calculators have an integration function that can handle basic integrals like this one. However, it is always recommended to understand the steps and concepts behind the calculation rather than solely relying on a calculator.