# Integral involving a square root which I can't work out

• sandysip
In summary, an integral is a mathematical concept used to find the total value of a function over a given range by representing the area under a curve. To solve an integral involving a square root, one can use a technique called substitution. However, integrals involving square roots can be challenging and may require advanced mathematical techniques. Common mistakes when solving these integrals include forgetting to use substitution, incorrectly applying integration rules, and making arithmetic errors. Some tips for solving integrals involving square roots include practicing substitution, reviewing integration rules, and double-checking for mistakes. It can also be helpful to break the integral down into smaller parts.
sandysip

## Homework Statement

Hi, I'm stuck on the following integral.

∫ y / (√(a(y^2)-c)) dy

where a and c are constants

## The Attempt at a Solution

I've tried using standard integrals involving square roots in the denominator, but I'm unsure what to do with the y on the numerator.

Any help would be appreciated!

Hint: Write the integrand as the derivative of a function of the form √(______).

## 1. What is an integral?

An integral is a mathematical concept that represents the area under a curve. It is used to find the total value of a function over a given range.

## 2. How do you solve an integral involving a square root?

To solve an integral involving a square root, you can use a technique called substitution. This involves substituting a variable for the expression inside the square root, then solving the integral using traditional integration techniques.

## 3. Why can't I work out this integral?

Integrals involving square roots can be challenging to solve because they often require advanced mathematical techniques and manipulations. It is also possible that the integral is unsolvable using traditional methods.

## 4. What are some common mistakes when solving integrals involving square roots?

Some common mistakes when solving integrals involving square roots include forgetting to use substitution, incorrectly applying integration rules, and making arithmetic errors.

## 5. What are some tips for solving integrals involving square roots?

Some tips for solving integrals involving square roots include practicing substitution, reviewing integration rules, and double-checking your work for mistakes. It can also be helpful to break the integral down into smaller, more manageable parts.

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