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

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The integration problem involves solving the integral of 3/(1+4x)^0.5 from x=0 to x=2, which represents the area under the curve. The correct approach involves substituting u=1+4x, transforming the integral into 3/4*u^(-1/2)du with limits changing from 1 to 9. After applying the power rule, the integral can be evaluated to yield the result of 3. Users expressed difficulty in reaching this answer and shared methods for solving it, emphasizing the importance of proper substitution and application of integration techniques. The final answer confirms the area under the curve is indeed 3.
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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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If you let u=1+4x, then the integral becomes 3/4*u^(-1/2)du for u from 1 to 9.
 
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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