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For a function f(x) =2x .
∫f′(x)dx=\int_{ }^{ }f'\left(x\right)dx=∫f′(x)dx=
222
4x4x4x
2x+c2x+c2x+c
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
Is the sentence true or false?
Two primitive functions with the same derivative lead to the same family of curves.
True
False
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
If F(x) is primitive, the sum F(x) +c is __________ function, where c is constant .
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
∫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
The integral of the sum of two primitive functions is equal to the sum of integrals of the given functions.
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.