in this case, our cross-sections are parabolas of the form . but what is the area of this parabola that fits your constraints? recall that the area "under" the curve is given by the integral. so graph the curve for arbitrary . find the intercepts and all that. now find the area under this curve. we see the area will be given by: .
Now, when you get the integral, replace the a with x, since in this case, a = x (the parabola is bounded by y = x, so the height is given by x, so that a = x since a is the height of our parabola above the x-axis). then go to the volume formula i gave you above to find the answer. x ranges from 0 up to 10