How Can I Integrate sqrt(2+2sin(x))?

  • Thread starter lostinhere
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In summary, integration is a mathematical process of finding the area under a curve defined by a function. To integrate a square root function, you can use the substitution method or integration by parts. The steps to integrate sqrt(2+2sin(x)) are using substitution, rewriting the function, integrating using the power rule, and replacing the substituted variable. A calculator can be used to solve the integral, but may not be able to solve more complex integrals. The purpose of integrating sqrt(2+2sin(x)) is to find the total value or quantity represented by the function, which can be useful in solving real-world problems.
  • #1
lostinhere
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I'm having trouble with this. Can anyone help me integrate

sqrt(2+2sin(x))

??

Thanks
 
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  • #2
lostinhere said:
sqrt(2+2sin(x))
Can you out it into a different form first?

The Bob (2004 ©)
 
  • #3
Other than
sqrt(2)*sqrt(1+sin(x))

I'm stuck
 
  • #4
HINT:Make the substitution

[tex] \tan\frac{x}{2}=t [/tex]

Daniel.
 
  • #5
Can you be more specific please?
 
  • #6
Transform the integral (make a change of variable).

[tex] \sqrt{2}\int \sqrt{1+\sin x} \ dx [/tex]

[tex] x=2\arctan t [/tex]

Daniel.
 
  • #7
hello there

sqrt[1+sinx]=[(cosx)^2]/[sqrt[1-sinx]]

see what you could do with that if it helps

steven
 

1. What is the definition of integration?

Integration is a mathematical process that involves finding the area under a curve defined by a function. It is the reverse process of differentiation and is used to solve problems related to finding the total value or quantity represented by a function.

2. How do you integrate a square root function?

To integrate a square root function, you can use the substitution method or integration by parts. In this case, for the function sqrt(2+2sin(x)), you can use the substitution u = 2 + 2sin(x) to simplify the integration process.

3. What are the steps to integrate sqrt(2+2sin(x))?

The steps to integrate sqrt(2+2sin(x)) are as follows:
1. Use the substitution u = 2 + 2sin(x) to simplify the function.
2. Rewrite the function in terms of u.
3. Integrate the function using the power rule.
4. Replace the u with the original expression to get the final answer.

4. Can you use a calculator to integrate sqrt(2+2sin(x))?

Yes, you can use a calculator with an integration function to solve the integral of sqrt(2+2sin(x)). However, it is important to note that calculators may not be able to solve more complex integrals and may not provide the steps to reach the final answer.

5. What is the purpose of integrating sqrt(2+2sin(x))?

The purpose of integrating sqrt(2+2sin(x)) is to find the total value or quantity represented by the function over a given interval. It can be used to solve real-world problems related to finding the area, volume, or accumulated value of a changing quantity.

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