## Question

###### Theorem 3.4. Suppose each of f and g is integrable over the interval [a, b] then:for a number c cf is integrable over the interval [a, b]; furthermorefaaef = c f2. f + g is integrable over the interval [a,b]; furthermorefa f +9 = fa a,b] s+ f a.6]f . 9 is integrable over the interval [a,b]; furthermore if each of f' and is COIlinuous (henf() . 9(6) f(a)g(a) = Jan" f .9 + Jan f'4. If f(r) # 0,x â‚¬ [a,b], $ is integrable over the interval [a, b]. If range(g) â‚¬ domain( f) then f o

Theorem 3.4. Suppose each of f and g is integrable over the interval [a, b] then: for a number c cf is integrable over the interval [a, b]; furthermore faaef = c f 2. f + g is integrable over the interval [a,b]; furthermore fa f +9 = fa a,b] s+ f a.6] f . 9 is integrable over the interval [a,b]; furthermore if each of f' and is COIlinuous (hen f() . 9(6) f(a)g(a) = Jan" f .9 + Jan f' 4. If f(r) # 0,x â‚¬ [a,b], $ is integrable over the interval [a, b]. If range(g) â‚¬ domain( f) then f o g is integrable over an interval in the domain of g. Comments [re Theorem 3.4]: One of these is false (s0 it's not a theorem (yet) ) , add sufficient conditions for it to be true

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