Find the area common to the inside of the cardioid $r = 1+\sin \theta$ and the outside of the cardioid $r = 1 + \cos \theta$.

Question

Function Plotter graph:

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I think the formula is

$$A = \frac 1 2 \int_{\alpha}^{\beta} (\text{outer})^2 - (\text{inner})^2 d\theta$$

where $\alpha, \beta$ are where they intersect in $[0, 2\pi]$.

This is what I got based on that

$$A = \frac 1 2 \int_{3\pi/4}^{5\pi/4} (1+\sin \theta)^2 - (1+\cos \theta)^2 d\theta$$

Is that right?