Let and . Which of the following statements is…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

F(x)=\ln|x|+x^{2}

and

G(x)=\ln|x|+x^{2}+7

. Which of the following statements is true? (a) Both

F

and

G

are antiderivatives of

f(x)=\dfrac{1}{x}+2x

and

F(x)-G(x)=7

for all

x\ne0

. (b) Both

F

and

G

are antiderivatives of

f(x)=\dfrac{1}{x}+2x

and

F(x)-G(x)=-7

for all

x\ne0

. (c) Both

F

and

G

are derivatives of

f(x)=\dfrac{1}{x}+2x

. (d) Only

G

is an antiderivative of

f(x)=\dfrac{1}{x}+2x