Find the antiderivative F(x) with F′(x)=f(x) and F(0)=2 f(x)=−7x F(x)=________?

anti-derivative

#1

Find the antiderivative F(x) with F′(x)=f(x) and F(0)=2
f(x)=−7x F(x)=________?

Answer:

F(x) = (-7/2)x^2 + CONSTANT
where F(0) = 2
2 = (-7/2)0^2 + CONSTANT
or
2 = 0 + CONSTANT, so CONSTANT = 2

F(x) = (-7/2)x^2 + 2