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Complete this statement:
If ∫\int_{ }^{ }∫ [ f (v)-g(v)]dv = ___________.
∫f(v)dv\int_{ }^{ }f\left(v\right)dv∫f(v)dv
∫f(v)dv+∫g(v)dv\int_{ }^{ }f\left(v\right)dv+\int_{ }^{ }g\left(v\right)dv∫f(v)dv+∫g(v)dv
∫f(v)dv−∫g(v)dv\int_{ }^{ }f\left(v\right)dv-\int_{ }^{ }g\left(v\right)dv∫f(v)dv−∫g(v)dv
If F =∫\int_{ }^{ }∫ f (v)dv and G =∫\int_{ }^{ }∫ g(v)dv then F - G = ___________.
∫(f+g)(v)dv\int_{ }^{ }\left(f+g\right)\left(v\right)dv∫(f+g)(v)dv
∫(af+g)(v)dv\int_{ }^{ }\left(af+g\right)\left(v\right)dv∫(af+g)(v)dv
∫(f−g)(v)dv\int_{ }^{ }\left(f-g\right)\left(v\right)dv∫(f−g)(v)dv
If f (x)=5x3 and g(x)=-7x2 then ∫[f(x) - g(x)] dx = ___________.
54x4+ex+c\frac{5}{4}x^4+e^x+c45x4+ex+c
54x4+73x3+c\frac{5}{4}x^4+\frac{7}{3}x^3+c45x4+37x3+c
54x4+73x3+x+c\frac{5}{4}x^4+\frac{7}{3}x^3+x+c45x4+37x3+x+c
Is the sentence true or false?
The antidifferentiation of k f(x) is equal to k times the antidifferentiation of f(x),where k is a scalar.
True
False
If ∫\int_{ }^{ }∫ [ f (v)+g(v)]dv = ___________.
∫(f−g)vdv\int_{ }^{ }\left(f-g\right)vdv∫(f−g)vdv
If f (x)=ex then ∫[10 f(x) ] dx = ___________.
x22+ex+c\frac{x^2}{2}+e^x+c2x2+ex+c
ex+ce^x+cex+c
10ex+c10e^x+c10ex+c
If f (x)=Sinx and g(x)=loglogx then ∫[f(x) + g(x)] dx = –cosx-xloglogx+c
If f (x)=1 and g(x)=ex then ∫[f(x) - g(x)] dx = ___________.
x22−ex+c\frac{x^2}{2}-e^x+c2x2−ex+c
x−ex+cx^{ }-e^x+cx−ex+c
ex−x+ce^x-x+cex−x+c
k f (v)dv = ___________.
k∫f(v)dvk\int_{ }^{ }f\left(v\right)dvk∫f(v)dv
k2∫f(v)dvk^2\int_{ }^{ }f\left(v\right)dvk2∫f(v)dv
If g(x)=Cosx then ∫[5g(x) ] dx = ___________.
5sinx+c5\sin x+c5sinx+c
15sinsinx+c15\sin\sin x+c15sinsinx+c
It is done.