How to do these two problems?

[Complete]

Find the indefinite integral

1) ∫(2/cuberoot(3x) dx

and

2) Use the limit process to find the area of the region between the graph of y=x^2+3 and x axis over the interval [0,2]. Change in x is 2/n

For this one I got 4 but I was told that is incorrect

 

[Deleted member 4993]

Find the indefinite integral

1) ∫(2/cuberoot(3x) dx

substitute

u = x^1/3

du =(1/3)* x^-2/3 dx

dx = 3u²du

Now continue......

and

2) Use the limit process to find the area of the region between the graph of y=x^2+3 and x axis over the interval [0,2]. Change in x is 2/n

For this one I got 4 but I was told that is incorrect

Please post your work - so that we know exactly where you would need help.

.

 

[Complete]

For the second question, I redid it and got 16 this time, I am unsure if I did it right.

lim n-->inf of sigma [f(a+i(b-a)/n) * 2/n]

I get it into that formula, and get it down to [f(2i/n)*2/n]

Then I get, plugging into the formula [((2i/n)^2 + 3) * 2/n]

I remove the 2/n and get

2/n sigma [9i^2/n + 3)

I distribute the sigma and get

2/n(4/n((n(n+1)(2n+1))/6) + 3n)

and from doing the algebra, I end up with (36n^2+16n^3+24n^2+8n) / 6n^2

I use end behavior and find the highest exponent and divide it by all the terms and get 16.