How Do You Solve the Integral of √x/(1+√x) from 0 to 4?

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Homework Help Overview

The discussion revolves around evaluating the integral of √x/(1+√x) from 0 to 4, which falls under the subject area of calculus, specifically integral calculus.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore various substitution methods and algebraic manipulations to simplify the integral. There are suggestions to perform polynomial division and to adjust the numerator for easier integration.

Discussion Status

The discussion is active with multiple participants offering different strategies for approaching the integral. Suggestions include simplifying the denominator and manipulating the numerator, indicating a collaborative exploration of methods.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the types of solutions or methods they can employ.

ddr
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Homework Statement



4
∫ √x/(1+√x)
0

Homework Equations





The Attempt at a Solution



t=√x ; x=t^2 ; dx= 2t

2
∫ (2t^2)/(1+t)
0

and now?
thanx
 
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Simplify your denominator with another substitution.
 
Bring the 2 outside the integral and then add and subtract 1 in the numerator.
 
First subtract and then add 1 in the numerator.

Daniel.
 
Hi ddr,

Perform polynomial algebraic division and integrate the result directly.
 

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