Integration Problem: Solving 3/(1+4x)^0.5 from x=0 to x=2

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In summary, the conversation discusses a problem with finding the area under a curve for the equation 3/(1+4x)^0.5 between x=0 and x=2. The individual tried rewriting the equation and using substitution, but could not find the correct answer. They are seeking help to find the solution.
  • #1
PhyStan7
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Hi all, I am having a problem with an integration.


Solve the integration 3/(1+4x)^0.5 between x=0 and x=2. Basically find the area under a curve of the equation between x=0 and x=2.

I know the answer is 3 but can't get to it. I tried rewriting it as 3(1+4x)^-0.5 and solving bu got stupid answers like 15. and 21 to lots of dp. I can't find the mark scheme to the past paper i am doing anywhere on the internet so can't find a solution. Help would be much appreciared, thanks
 
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  • #2
If you let u=1+4x, then the integral becomes 3/4*u^(-1/2)du for u from 1 to 9.
 
  • #3
Random Variable said:
If you let u=1+4x, then the integral becomes 3/4*u^(-1/2)du for u from 1 to 9.

3/(1+4x)^0.5 = 3 * (1+4x)^(-0,5)

Now you can use the common powers law with the exponent (-0,5).
Adding 1 to this gives (0,5).
 
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FAQ: Integration Problem: Solving 3/(1+4x)^0.5 from x=0 to x=2

What is a simple integration problem?

A simple integration problem is a mathematical problem that involves finding the indefinite or definite integral of a function. This involves finding the area under the curve of the function within a certain interval.

What is the purpose of solving simple integration problems?

The purpose of solving simple integration problems is to determine the total change or accumulation of a function over a given interval. This can be used in various applications such as finding the displacement of an object, calculating the work done by a force, or determining the total cost of production.

How do you solve a simple integration problem?

To solve a simple integration problem, you can use various techniques such as substitution, integration by parts, or using specific integration formulas. First, identify the function and its limits, then use the appropriate technique to find the integral. Finally, evaluate the integral at the given limits to get the final answer.

What are some common mistakes to avoid when solving simple integration problems?

Some common mistakes to avoid when solving simple integration problems include forgetting to use the chain rule, incorrect substitution, and missing negative signs. It is also important to check for any mistakes in algebraic manipulations and to be aware of any special cases where specific integration techniques should be used.

Can simple integration problems have multiple solutions?

No, simple integration problems have a unique solution. However, there may be different ways to arrive at the same solution depending on the integration technique used. It is important to check your answer to ensure it is correct and to use proper notation when writing the final solution.

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