JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q23

← JEE Main 2022 · 25 Jun · Shift 2

MathematicsInteger+4 / -1Question 23 of 90

The value of $b>3$ for which $12\displaystyle\int_3^b\frac1{\left(x^2-1\right)\left(x^2-4\right)}dx=\log_e\left(\frac{49}{40}\right)$ , is equal to ______.

Your answer

Answer and worked solution

Official answer: 6

Partial fractions. $\dfrac1{(x^2-1)(x^2-4)}=\dfrac13\left(\dfrac1{x^2-4}-\dfrac1{x^2-1}\right)$ .

Antiderivative. $12\displaystyle\int=\log_e\frac{(x-2)(x+1)^2}{(x+2)(x-1)^2}$ ; at $x=3$ it is $\log_e\frac45$ .

Solve. We need the value $\log_e\frac{49}{50}$ at $b$ ; $b=6$ gives $\dfrac{4\cdot49}{8\cdot25}=\dfrac{49}{50}$ .

Answer: 6

Topics:Fundamental theorem of calculus Partial fractions

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JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 23