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ToxicBug
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Could anyone evaluate this integral for me? I got it in an exam and didn't know how to do it.
[tex]\int\sqrt{x-x^2}[/tex]
[tex]\int\sqrt{x-x^2}[/tex]
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what do I mean? I thought I make it very clear already!What do you mean? Can you evaluate it completely showing the steps?
Integration is a mathematical concept that involves finding the area under a curve. It is used to solve problems involving rates of change, such as finding the velocity or acceleration of an object.
Integration and differentiation are inverse operations. While differentiation finds the rate of change of a function, integration finds the original function from its rate of change. In other words, differentiation finds the slope of a curve, while integration finds the area under a curve.
The most common methods of integration are substitution, integration by parts, and partial fractions. Substitution involves substituting a variable with a simpler expression, integration by parts involves using the product rule in reverse, and partial fractions is used to integrate rational functions.
Integration is used in many fields such as physics, engineering, economics, and statistics. It can be used to calculate the work done by a force, the amount of heat transferred in a chemical reaction, or the probability of an event occurring.
Some common applications of integration include finding the area under a curve to calculate displacement, velocity, or acceleration, calculating volume of irregular shapes, and finding the average value of a function over a certain interval.