Integral with circular coordinates

[vivid tulip]

This integral is supposed to give 15pi/16 but I keep getting 7pi/6. The integral is the volume between two spheres with 1 radius and 2 radius in the first eight of the 3d plane

[ashen lodge]

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[old zodiac]

$$ \int _1^2 \int _0^{\pi /2} \int _0^{\pi /2} r^2 \sin \theta d\theta d\phi dr $$

[calm lantern]

aL

[old zodiac]

@vivid tulip

7 pi / 6 is correct

we can double check by subtracting and dividing

$$ V_2-V_1 = \frac{4}{3}\pi (2^3 - 1^3) = \frac{56}{6}\pi $$

[calm lantern]

aL