Integration of y * sqrt function

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Homework Help Overview

The problem involves the integration of the function 3/8 * ∫ (y^3) * √((y^4)+9) dy, evaluated from 0 to 2. The context appears to be related to techniques of integration, possibly within a calculus framework.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of substitution as a potential method for solving the integral, with one suggesting u = y^4 + 9 as a substitution. There is also mention of reviewing various integration techniques.

Discussion Status

Some participants have shared their attempts at the problem, with one indicating that a substitution worked well for them. Others have provided suggestions for reviewing integration techniques, indicating a collaborative exploration of the topic.

Contextual Notes

There is mention of double integrals and the challenges associated with ordinary substitutions, suggesting that the problem may involve more complex integration techniques.

Emilyd
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Homework Statement



given: 3/8 * ∫ (y^3) *√((y^4)+9) dy the integral is from 0 - 2



Homework Equations





The Attempt at a Solution



I have attempted the problem so far, it was a double integration and it is right up to here. I just can't figure out how to integrate this part.
 
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Emilyd said:

Homework Statement



given: 3/8 * ∫ (y^3) *√((y^4)+9) dy the integral is from 0 - 2



Homework Equations





The Attempt at a Solution



I have attempted the problem so far, it was a double integration and it is right up to here. I just can't figure out how to integrate this part.
Looks like an ordinary substitution would work - u = y^4 + 9 ==> du = 4u^3*du
 
Thankyou! worked a treat.
 
So if you're working with double integrals and having trouble with ordinary substitutions, I would advise you to go back and review the integration techniques such as substitution, trig substitution, integration by parts, and partial fractions.
 

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