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What is another name for a primitive function?
Definite integral
indefinite integral
Is the sentence true or false?
The primitive function is also called the indefinite integral.
True
False
What is the antiderivative of f(x)=2x .f\left(x\right)=2x\ .f(x)=2x .
x+cx+cx+c
x2+cx^2+cx2+c
2x+c2x+c2x+c
If F a primitive function of f the which one of following 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
If F is a primitive of f, so is F + c for any constant c.
If G a primitive function of g the which one of following is true?
∫g =G+C\int_{ }^{ }g\ =G+C∫g =G+C
g′=gg'=gg′=g
∫G=G\int_{ }^{ }G=G∫G=G
Primitive function of a constant function is zero.
Primitive functions may have served as a derivative.
For f(x)=3x2f\left(x\right)=3x^2f(x)=3x2 ,the primitive function F(f(x))=x3+c .F\left(f\left(x\right)\right)=x^3+c\ .F(f(x))=x3+c .
For f(x)=x+3x2f\left(x\right)=x+3x^2f(x)=x+3x2 ,the primitive function F(f(x))=x22+cF\left(f\left(x\right)\right)=\frac{x^2}{2}+cF(f(x))=2x2+c .
It is done.