# Whats the intergral of sqrt(25-9x^2)?

• grizz45
In summary, the person is asking for the integral of sqrt(25-9x^2) and the expert recommends factoring out a 9 from under the radical and using trig substitution, followed by checking the result on a website. The expert also points out that there is no such word as "intergral" in English or German, and clarifies the difference between the "inter-graal" and the "grail."
grizz45
Whats the intergral of sqrt(25-9x^2)?

Factor out a 25 from under the radical and use trig substitution.

rochfor1 said:
Factor out a 25 from under the radical and use trig substitution.
I would factor out 9 from under the radical to give 1/3*sqrt(25/9 - x^2) and use trig substitution. After I got the antiderivative I might then go to the Wolfram site to check my result against theirs.

BTW, there is no such word as "intergral."

Mark44 said:
BTW, there is no such word as "intergral."
Nonsense.

The intergral, or rather, in German, Der Inter-Graal, was the cup Jesus drank from in the wedding in Kanaan(?) where he made water into wine.

This to distinguish it from the grail, or Der Graal, the cup he drank from at the last Supper.

OK, let me be more specific: there's no such word as "intergral" in English. And it appears that there is no such word in German, either. Inter-Graal != intergral.

## 1. What is an integral?

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

## 2. What does the notation "sqrt" mean?

"sqrt" is a mathematical notation that stands for the square root of a number. For example, sqrt(25) equals 5.

## 3. How do you find the integral of a function?

To find the integral of a function, you must first determine the antiderivative of the function. Then, you can use the fundamental theorem of calculus to calculate the integral by plugging in the upper and lower limits of the interval.

## 4. What is the purpose of calculating the integral of sqrt(25-9x^2)?

The integral of sqrt(25-9x^2) can be used to find the area under the curve of the function. It can also be used to find the total value of the function over a given interval.

## 5. Are there any specific methods for solving this integral?

Yes, there are various methods for solving integrals, such as substitution, integration by parts, and trigonometric substitution. The appropriate method to use depends on the complexity of the function.

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