JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

If $f\left(\dfrac{3x-4}{3x+4}\right)=x+2$ , $x\ne-\dfrac43$ , and $\displaystyle\int f(x)\,dx=A\log|1-x|+Bx+C$ , then the ordered pair (A, B) is equal to :

(where C is a constant of integration)

\left(\dfrac83,\dfrac23\right)

\left(-\dfrac83,\dfrac23\right)

\left(-\dfrac83,-\dfrac23\right)

\left(\dfrac83,-\dfrac23\right)

Answer and worked solution

Official answer: B

Put $t=\dfrac{3x-4}{3x+4}$ , so $x=\dfrac{4(1+t)}{3(1-t)}$ and
$f(t)=x+2=\frac23+\frac{8/3}{1-t}.$
Integrating, $\displaystyle\int f\,dt=-\frac83\log|1-t|+\frac23t+C$ , so $(A,B)=\left(-\frac83,\frac23\right)$ .

Topics:Substitution Composition and inverse functions

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 74