Solving Difficult Integral Homework Equation w/ Limits 0 to a

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In summary, the conversation is about solving the integral a^2 f(x) dx with limits from 0 to a. The proposed solution is 1/2 Integral (a-x)^2 f(x) dx, but it is questioned because a should be a constant with respect to x. More information about f(x) is needed to fully evaluate or simplify the expression.
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Integral8850
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Homework Statement



Integral a^2 f(x) dx .....limits are 0 to a

I know the answer is... 1/2 Integral (a-x)^2 f(x) dx


Homework Equations





The Attempt at a Solution


I do not know how to approach this problem. I have tried to use the fundamental theorem of calculus its not working. This is a review for a test. Thanks in advance.
 
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  • #2
That can't be your answer. a is the upper bound and hence must be a constant with respect to x, so you just take the a^2 out of the integral to the front. Other than that simplification, there's nothing we can do to evaluate or simplify that expression without knowing more about what f(x) is.

Are you sure you have written down the question exactly as it was given?
 

FAQ: Solving Difficult Integral Homework Equation w/ Limits 0 to a

What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the total accumulation of a function over a given interval.

What are the limits in an integral?

Limits in an integral are the boundaries of the interval over which the function is being integrated. In this case, the limits are 0 and a, meaning the integral is being calculated from 0 to a.

How do I solve a difficult integral?

Solving a difficult integral involves using various techniques such as substitution, integration by parts, or trigonometric identities. It also requires practice and familiarity with different types of integrals.

What is the purpose of using limits in an integral?

Limits in an integral help define the domain over which the function is being integrated. It also allows for more precise calculations and helps to avoid any undefined or infinite values.

What are some common mistakes to avoid when solving an integral with limits?

Some common mistakes to avoid include forgetting to include the constant of integration, not properly evaluating the limits, and making errors in algebraic simplification. It is important to double-check all steps and use proper notation when solving integrals.

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