How to 3D plot a 2 parameter function that includes a definitive integral, using Wolfram Alpha?

Question

I'm trying to plot the following function using Wolfram Alpha:

I have used the following natural language query:

plot (x^2 − ( Integrate sqrt(1 − t) ) , for x from 0 to 5, for y from -4 to 1)

I'm struggling to add in the boundaries for the definitive integral.

What's the correct query?

Answer 1

I've tried several different ways and can't yet get WA to do it in one step.

But I can get it to do it in two steps.

First

x^2-Integrate sqrt(1-t),{t,0,y}

returns

x^2+2/3((1-y)^(3/2)-1) for Re(y)<=1 or y not element R

and your range for y satisfies that condition

Next

plot x^2+2/3((1-y)^(3/2)-1),{x,0,5},{y,-4,1}

and it appears you are done