Inegration with square roots - calc 1

In summary, integration with square roots is a mathematical technique used to find the antiderivative or indefinite integral of a function containing a square root. This can be done using the substitution method or integration by parts. The general formula for integrating a square root function is ∫√(x)dx = 2/3x^(3/2) + C. When dealing with complex square root expressions, simplification techniques or trigonometric substitutions can be used. Real-life applications include calculating area, volume, and production rates in physics, engineering, and economics.
  • #1
Aimee79
2
0
1. Homework Statement [/b]
∫x/√(x-1)dx

2. Homework Equations [/b]
I'm just stumped. I have tried u substituion with
u=√(x-1)
x=u^2+1

((u^2+1)/u)du
=(u+1/u)du

but it doesn't seem to work and I can't integrate 1/u.

I just don't know where to go with this any help would be greatly appreciated.

Aimee
 
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  • #2
If I were doing this question, I wouldn't make the substitution you made, but would instead use the substitution u=x-1.
 

1. What is integration with square roots?

Integration with square roots is a mathematical technique used to find the antiderivative or indefinite integral of a function containing a square root. It involves reversing the process of differentiating a function and is an important concept in calculus.

2. How do you integrate a function with a square root?

To integrate a function with a square root, you can use the substitution method or the integration by parts method. In the substitution method, a variable is substituted for the expression inside the square root, and the integral is then solved using u-substitution. In the integration by parts method, the integral is split into two parts and each part is integrated separately.

3. What is the general formula for integrating a square root function?

The general formula for integrating a square root function is ∫√(x)dx = 2/3x^(3/2) + C. This formula can be derived by using the power rule for integrals, where the exponent is multiplied by the reciprocal of the new exponent and then the constant of integration is added.

4. How do you handle complex square root expressions when integrating?

When dealing with complex square root expressions, the first step is to try to simplify the expression by factoring out perfect squares. If this is not possible, you can use trigonometric substitutions or integration by parts to solve the integral. It is important to be familiar with algebraic manipulations and trigonometric identities when handling complex square root expressions.

5. What are some real-life applications of integration with square roots?

Integration with square roots has many real-life applications in fields such as physics, engineering, and economics. It can be used to calculate the area under a curve, which is important in determining velocity, acceleration, and displacement in physics. In engineering, it can be used to calculate the volume of irregularly shaped objects. In economics, it can be used to calculate the average production rate of a company.

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