How Do You Evaluate the Integral of (x^2 + y^2)^(-3/2) with Respect to y?

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In summary, the conversation is about a person seeking help with evaluating a specific integral. They have attempted the problem but are unsure if their solution is correct. The person providing assistance suggests using a trig substitution and offers a hint. The original person thanks them and mentions needing to review their trig substitutions and integration by substitution.
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crossroads
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I took calc a year ago, and already am apparently rusty. I'm trying to figure out how to evaluate the integral: [tex] \int (x^2+y^2)^(^-^3^/^2) dy[/tex]. This isn't a homework problem by the way, its actually an example problem in the book, but they don't show step by step how they got to the answer. If someone could go through this step by step that would be really nice :). You're just supposed to treat the x^2 as a constant, right? I get as far as: [tex](-2 (x^2+y^2)^(^-^1^/^2^)) / 2y [/tex] but I'm not even sure if that much is correct. Thanks for any help.
 
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Welcome to PF!

Hi crossroads! Welcome to PF! :smile:

(have an integral: ∫ and a square-root: √ and try using the X2 tag just above the Reply box :wink:)

Yes, x2 is a constant.

No, it isn't -1/y√(x2 + y2).

Hint: try a trig substitution. :wink:​
 
  • #3
Thanks for the hint and the welcome. I got the answer, but it looks like I need to review my trig substitutions and integration by substitution.
 

FAQ: How Do You Evaluate the Integral of (x^2 + y^2)^(-3/2) with Respect to y?

How do I find the integral of a function?

Finding the integral of a function involves using techniques such as integration by substitution, integration by parts, or the fundamental theorem of calculus. It can also be helpful to use a graphing calculator or software to help visualize the function and its integral.

What is the purpose of finding the integral of a function?

The integral of a function represents the area under the curve of the function. It can also be used to calculate displacement, velocity, and acceleration in physics problems. Additionally, the integral can help solve optimization problems in mathematics.

Can I solve an integral without knowing the function?

Yes, it is possible to solve an integral without knowing the exact function. This can be done by using numerical methods such as the trapezoidal rule or Simpson's rule to approximate the integral. However, these methods may not always yield an accurate result.

How do I know if my integral is correct?

To check if your integral is correct, you can differentiate the result and see if it matches the original function. This is known as the "reverse product rule." You can also use a graphing calculator or software to graph both the function and its integral and compare them visually.

Are there any tips for solving integrals more efficiently?

Some tips for solving integrals more efficiently include recognizing common patterns and applying appropriate integration techniques, practicing regularly to improve problem-solving skills, and using online resources or textbooks for additional practice and guidance.

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