Question 1:
True or False. If F(x) is an antiderivative of f(x) and c is any constant, then F(x) + c is also an antiderivative of f(x).
Answer :
True.
Differentiate F(x) + c.
Question 2:
True or False. If F(x) is an antiderivative of f(x), then
(1/a) F(ax) is an antiderivative of f(ax).
Answer :
True.
Let u = a x and Differentiate (1/a) F(ax) with respect to x
d/dx( (1 / a) F(a x) )
= (1 / a) d(u) / dx dF/dU
= (1/a) a f(u) = f(a x)
Question 3:
True or False. An antiderivative of function f plus an antiderivative of function g is an antiderivative of function f + g.
Answer :
True. Use the rule of diferentiation to differentiate F + G, where F is the antiderivative of f and G is the antiderivative of g, and see that you can get f + g.
Question 4:
True or False. An antiderivative of function f divided by an antiderivative of function g is an antiderivative of function f / g.
Answer :
False. Use the rule of diferentiation to differentiate F / G, where F is the antiderivative of f and G is the antiderivative of g, and see that you cannot get f / g.
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