The answer is B. Can anyone plz explain why A,C,D,E are wrong and B is right? Su
ID: 2894154 • Letter: T
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The answer is B. Can anyone plz explain why A,C,D,E are wrong and B is right?
Suppose F(x) and G(x) are both antiderivatives of f(x) on some I. Hos are F(x) and G(x) related on the interval I? (This question is multiple choice, here are options:) A. F(x) + G(x) is constant. B. F(x) - G{x) is constant. C. The integrals integral^x_0 F(t)dt and integral^z_0 G(t)dt are equal. D. The derivatives d/dx F(x) and d/dx G(x) differ by some non-zero constant. (g) There is no relation between two different antiderivatives of a function.Explanation / Answer
given F(x),G(x) are antiderivatives of f(x)
=>F'(x)=f(x) ,G'(x)=f(x)
=>F'(x)-G'(x)=f(x)-f(x)
=>F'(x)-G'(x)=0
=>[F'(x)-G'(x)] dx =0 dx
=>F(x)-G(x) =c , where c is constant
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a)F(x)+G(x) is a function of variable x
c)F(x),G(x) are different , so [0 to x]F(t) dt ,[0 to x]G(t) dt are different
d)F(x),G(x) are antiderivatives of f(x)
=>d/dxF(x)=f(x) ,d/dxG(x)=f(x)
=>d/dxF(x) -d/dxG(x)=0
e)there is a relation as shown above. they differ by a constant
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