Question

a) If F(x) is an antiderivative of f(x) and G(x) = F(x) +2, then G(x) is an antiderivative of f(x).
b) If F(x) is an antiderivative of f(x) and G(x) is an antiderivative of g(x), then F(x)*F(x) is an antiderivative of f(x)*g(x).

True or False?

Answer 1

try it and see

Answer 2

first one is evidently true, since the derivative of 2 is zero
try the second one with some easy functions like \(x^2\) and \(x^3\)

Answer 3

I'm thinking the second one is false based on what I have been getting.

Answer 4

yes of course it is false

Answer 5

Thank you!

Answer 6

yw