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Is the sentence true or false?
The integral of the sum of two primitive functions is equal to the sum of integrals of the given functions.
True
False
Fill in the blank:
If F(x) and G(x) are primitive, the sum F(x) +G(x) is __________.
Non primitive
primitive
definite
For two primitive functions f and g. If ∫(f(x)+g(x))dx\int_{ }^{ }\left(f\left(x\right)+g\left(x\right)\right)dx∫(f(x)+g(x))dx =
∫g(x)dx\int_{ }^{ }g\left(x\right)dx∫g(x)dx
∫f(x)dx\int_{ }^{ }f\left(x\right)dx∫f(x)dx +∫g(x)dx\int_{ }^{ }g\left(x\right)dx∫g(x)dx
∫f(x)dx\int_{ }^{ }f\left(x\right)dx∫f(x)dx +2∫g(x)dx\int_{ }^{ }g\left(x\right)dx∫g(x)dx
For a function f(x) =2x .
∫f′(x)dx=\int_{ }^{ }f'\left(x\right)dx=∫f′(x)dx=
222
4x4x4x
2x+c2x+c2x+c
For any real value of b,∫b.g(x)dx=\int_{ }^{ }b.g\left(x\right)dx=∫b.g(x)dx=
4∫g(x)dx4\int_{ }^{ }g\left(x\right)dx4∫g(x)dx
b∫g(x)dxb\int_{ }^{ }g\left(x\right)dxb∫g(x)dx
If F(x) is primitive, the sum F(x) +c is __________ function, where c is constant .
For two primitive functions f and g. If ddx∫f(x)dx=ddx∫g(x)dx\frac{d}{dx}\int_{ }^{ }f\left(x\right)dx=\frac{d}{dx}\int_{ }^{ }g\left(x\right)dxdxd∫f(x)dx=dxd∫g(x)dx . Then ∫f(x)dx=\int_{ }^{ }f\left(x\right)dx=∫f(x)dx=
∫2g(x)dx\int_{ }^{ }2g\left(x\right)dx∫2g(x)dx
∫g(x)dx+c\int_{ }^{ }g\left(x\right)dx+c∫g(x)dx+c
g(x)+cg\left(x\right)+cg(x)+c
∫24(x2)dx=\int_{ }^{ }24\left(x^2\right)dx=∫24(x2)dx=
24x24x24x
24∫(x2)dx24\int_{ }^{ }\left(x^2\right)dx24∫(x2)dx
242424
Two primitive functions with the same derivative lead to the same family of curves.
For two primitive functions f(x)=2x and g(x)=3x2.
∫((f(x)+g(x)))dx\int_{ }^{ }\left(\left(f\left(x\right)+g\left(x\right)\right)\right)dx∫((f(x)+g(x)))dx =
x3+cx^3+cx3+c
x2+x3+cx^2+x^3+cx2+x3+c
x2+cx^2+cx2+c
It is done.