# Why Is My Calculation of the Antiderivative for sqrt(20-x) Incorrect?

• hekoshi
In summary, The correct antiderivative for sqrt(20-x) from 0 to 20 is -(2/3)(20-x)^(3/2). The mistake in the previous attempt was using the sqrt function instead of the exponent of 3/2. The area below the curve of the original equation is not 0 and the antiderivative function is not zero for x = 0. The correct evaluation should be F(b)-F(a)=-(2/3)(20-20)^(3/2)-(-(2/3)(20-0)^(3/2)), and not zero at both limits.
hekoshi
I can't seem to get this antiderivitive correct: sqrt(20-x) from 0 to 20.

I end up with -(2/3)(sqrt(20-x)^(3/2) which is zero evaluated at either of the two limits.

This is not correct since the area below the curve of the original equation is definitely not 0.

You shouldn't have sqrt in your answer since that's already accounted for in the 3/2 exponent. Also, the antiderivative functionis not zero for x = 0. Check it again.

Yes and also it is not zero at both the limits; it should work out now.

oops, i meant to write -(2/3)(20-x)^(3/2), but yeah, i didn't evaluate it correctly the first time. It should be:

F(b)-F(a)=-(2/3)(20-20)^(3/2)-(-(2/3)(20-0)^(3/2))

*Facepalm* I blame it on lack of sleep, haha.

thanks.

## 1. What is an antiderivative?

An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function. In other words, it is the opposite of finding the rate of change of a function.

## 2. How do I find an antiderivative?

To find an antiderivative, you need to use the power rule, product rule, quotient rule, and chain rule in reverse. You also need to add a constant of integration (C) to the end of the antiderivative to account for all possible solutions.

## 3. What is the difference between an antiderivative and an indefinite integral?

An antiderivative and an indefinite integral are essentially the same thing. The only difference is that an indefinite integral does not have limits of integration, which means it represents a family of functions rather than a specific function.

## 4. Can I use antiderivatives to solve real-world problems?

Yes, antiderivatives can be used to solve real-world problems, especially in physics and engineering. They are useful in determining the position, velocity, and acceleration of objects, as well as in calculating areas and volumes.

## 5. Is there a shortcut for finding antiderivatives?

Yes, there are some common antiderivatives that can be memorized to make the process faster. These include the antiderivatives of polynomial functions, trigonometric functions, and exponential functions. However, it is important to remember that not all functions have simple antiderivatives, and some may require more advanced techniques.

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