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[1FZ] Prerequisites:Riemann integral,[19Q].Let IβŠ†β„ open interval with 0∈I. Given f=f(x,y):IΓ—[0,1]→ℝ continuous, and such that also βˆ‚βˆ‚xf exists and is continuous, set

g(x)=∫01f(x,y)dy,

show that g is of class C1, and that

gβ€²(x)=∫01βˆ‚ βˆ‚xf(x,y)dy .

Solution 1

[1G0]

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