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fysiikka111
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Homework Statement
Integrate
(2rx-x2)1/2
with respect to x where r is a constant.
Homework Equations
The Attempt at a Solution
Thanks
The formula for integrating (2rx - x2)1/2 w.r.t. x and Constant r is ∫(2rx - x2)1/2 dx = (2/3)(2rx - x2)3/2 + C, where C is the constant of integration.
The process for integrating (2rx - x2)1/2 w.r.t. x and Constant r is to first rewrite the expression as √(2rx - x2) and then use the substitution u = 2rx - x2. This will result in du = (2r - 2x) dx. The integral can then be rewritten as ∫√u du, which can be solved using the power rule for integration.
The purpose of integrating (2rx - x2)1/2 w.r.t. x and Constant r is to find the area under the curve of the given function. This is useful for calculating physical quantities such as displacement, velocity, and acceleration in physics, as well as for solving various mathematical problems.
Some common applications of integrating (2rx - x2)1/2 w.r.t. x and Constant r include calculating the arc length of a curve, finding the volume of a solid of revolution, and determining the work done by a variable force. It is also commonly used in physics to calculate the total energy of a system.
Some tips for solving integrals involving (2rx - x2)1/2 w.r.t. x and Constant r include using substitution to simplify the expression, using trigonometric identities to rewrite the integral, and breaking the integral into smaller parts if possible. It is also important to remember the constant of integration when solving these types of integrals.