Compute the volume of the solid

[number0]

Homework Statement

Computer the volume of the solid bounded by the xz plane, the yz plane, the xy plane, the planes x = 1 and y = 1, and the surface z = x² + y²

Homework Equations

None.

The Attempt at a Solution

Since the solid is bounded by the xz plane, the yz plane, the xy plane, it is assumed that the values of x, y, and z all equal 0. And since x = 1 and y = 1, the limits of integration is:

0 $$\leq$$ x $$\leq$$ 1

0 $$\leq$$ y $$\leq$$ 1

Thus, the double integral is:

$$\int$$ $$\int$$ x² + y⁴ dA

and the limits of integration is 0 $$\leq$$ x $$\leq$$ 1, 0 $$\leq$$ y $$\leq$$ 1.

After calculating the integral, I got the answer $$\frac{8}{15}$$. Can anyone verify my work?

 

[Mark44]

Homework Statement

Computer the volume of the solid bounded by the xz plane, the yz plane, the xy plane, the planes x = 1 and y = 1, and the surface z = x² + y²

Homework Equations

None.

The Attempt at a Solution

Since the solid is bounded by the xz plane, the yz plane, the xy plane, it is assumed that the values of x, y, and z all equal 0. And since x = 1 and y = 1, the limits of integration is:

0 $$\leq$$ x $$\leq$$ 1

0 $$\leq$$ y $$\leq$$ 1

Thus, the double integral is:

$$\int$$ $$\int$$ x² + y⁴ dA

and the limits of integration is 0 $$\leq$$ x $$\leq$$ 1, 0 $$\leq$$ y $$\leq$$ 1.

After calculating the integral, I got the answer $$\frac{8}{15}$$. Can anyone verify my work?

That's what I get, too.

For future reference, here is the integral I evaluated, using LaTeX.
$$\int_{x = 0}^1 \int_{y = 0}^1 x^2 + y^4~dy~dx$$

Click the integral to see my LaTeX code.