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Is the sentence true or false?
If F is the antiderivative of f, then F + c is also is antiderivative for any constant c.
True
False
For f(t) = 9t2, the primitive function F(f(t)) = 3t3 + C .
For g(t) = t + 3t2 , the primitive function G(g(t)) = t2/2 + C .
What is the primitive function of f(x)=3x.
x+cx+cx+c
32x2+c\frac{3}{2}x^2+c23x2+c
2x+c2x+c2x+c
Primitive function of a constant function is zero.
What is another name for the antiderivative?
Definite integral
indefinite integral
If F is the primitive function of f, then which one of the following statements is true?
∫F=f+c\int_{ }^{ }F=f+c∫F=f+c
f′=ff'=ff′=f
∫f=F+c\int_{ }^{ }f=F+c∫f=F+c
The primitive function is also called the indefinite integral.
The fact that the function G is a the primitive function of g is denoted by :
∫g = G+c\int_{ }^{ }g\ =\ G+c∫g = G+c
g′=gg'=gg′=g
∫G=G\int_{ }^{ }G=G∫G=G
Primitive functions may have served as a derivative.
It is done.