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\[\int_b^a 3xdx\]
is this the question?

yes

wait its b,a

int 3x dx = 3/2 x^2 +C
evaluate in terms of a-b
3/2 a^2 - 3/2 b^2

|dw:1330414875053:dw|

\[\int ^b_a 3xdx = \frac32 x^2 +c = \frac32 a^2-\frac32b^2+C\]

but then what is the method of summation??