Solving an Intriguing Integral: x-1 in the First Quadrant

[Knissp]

Homework Statement

$$\int\int_R x-1 dA$$
R is the region in the first quadrant enclosed between y=x and y=x^3

Homework Equations

The Attempt at a Solution

I set up the bounds as follows: $$\int_{x=0}^1\int_{y=x^3}^x x-1 dydx$$

Integrating, I get -7/60, verified with CAS.

I thought this was an easy problem but my answer doesn't match the textbook (-1/2 but could be a misprint, right?) or did I somehow put the bounds of integration wrong?

 

[Dick]

It looks fine to me.

 

[arildno]

I agree with your answer