Determine if the statement is true or false.
The FTC says that if f is continuous on [a, b], then
Answer
FALSE. The functions are switched. Instead of
it should read
because the derivative has to go inside the integral. We also need f to be continuous on [a, b].
The FTC says that if s is continuous on [a,b], then
TRUE. The function name got changed from f to s, but that's no big deal. We integrate the rate of change to find the change in the original function.
The FTC says that if F' is continuous on [a,b] then
TRUE. This is the same as the version of the FTC that states if f is continuous on [a, b] and f = F', then
The FTC says that if f is continuous on [a, b] and f is the derivative of F, then
FALSE. The limits of integration are in the wrong order on the right-hand side. Instead of
it should be
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