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Which method of integration should I use to begin this problem?

$$\int_1^4\int_y^4\int_0^zz/(x^2+z^2)\,\mathrm{d}x\mathrm{d}z\mathrm{d}y$$

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    $\begingroup$ Step 1: draw a picture to understand the shape being integrated over. $\endgroup$
    – vadim123
    Nov 4, 2014 at 21:02

1 Answer 1

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Hint:

1) First draw the region of integration

2) As its presented, see if this helps

$$\int \frac{a}{a^2+x^2} dx= \arctan \Big(\frac{x}{a}\Big) + C$$

The answer is $\frac{9\pi}{8}$.

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