Question

Evaluate: ∫ ∫ ∫ sinpix cosy sin2z dydxdz
0, pi/2; 0,1;0, pi/2

Answer 1

just do them, one variable by one, treating the others as constants

Answer 2

You can also rearrange a triple integral:
\[\int\limits \int\limits \int\limits xyz ~ dxdydz \rightarrow \int\limits x~dx \int\limits y~dy \int\limits z~dz\]
BUT you can only do this if your groups contain on each single variable. If the variables start mixing (ex: Sin(xy)) then you cannot do this.

Answer 3

ALSO we can only do this if the LIMITS ARE CONSTANTS. If they contain another variable, then we cannot perform it this way. Additionally, we can only do this if the terms are being multiplied within the integrand. if we have x+y+z, we cannot split the integral. If we have (x+y)(x+z)y, we still cannot break up the integral.

Answer 4

(͡° ͜ʖ ͡°)

Answer 5

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Answer 6

@imqwerty

Answer 7

:)