- #1
WubbaLubba Dubdub
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Homework Statement
Let ##g(x) = \int_0^xf(t) dt## where ##f## is such that ##\frac{1}{2} \leq f(t) \leq 1## for ##t \in [0,1]## and ##\frac{1}{2} \geq f(t) \geq 0## for ##t \in (1,2]##. Then ##g(2)## belongs to interval
A. ##[\frac{-3}{2}, \frac{1}{2}]##
B. ##[0, 2)##
C. ##(\frac{3}{2}, \frac{5}{2}]##
D. ##(2, 4)##
Homework Equations
The Attempt at a Solution
I got ##g'(x) = f(x)## and using this and the definite integral given, i have ##g(0) = 0##
I didn't really know where to go from here, so I tried making a graph (sort of) using the minimum and maximum slopes of the function in the given intervals and found an area in which, I think the function will exist, with the interval for ##g(2)## being ##[\frac{1}{2},\frac{3}{2}]##.
This isn't present in the options...Can someone please point out my mistakes and help me get the answer.
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