Evaluating def. int.: int[0,1] [(2x + 1) sqrt(x^2 + x)] dx

[cmnalo]

∫(2x + 1) square root of (x^2 +x) dx [0,1]

I know I should probably use the substitution method but I'm not sure whether to make u = 2x + 1 or u= x^2 +x?


Answer: 4 square root of 2 / 3

 

[Unco]

Taking u = x^2 + x, then du = 2x + 1 dx . It should be clear that this is advantageous.

 

[cmnalo]

so..

∫ (squareroot of u) (du) [0,1]

∫u^1/2 du

2/3u^3/2

2/3(t+1)^3/2 [0,1]

[2/3(1 +1)^3/2] - [2/3(0 +1)^3/2]

Is this looking correct?

 

[cmnalo]

I'm still having trouble with this problem can anyone assist.
Thanks

 

[pka]

All you have to do is find
\(\displaystyle \L \int\limits_0^2 {\sqrt u du} .\)