QJEEM24Ma7ba7: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7ba7 Solution: lim x → π 2 ⁡ ( 1 ( x − π 2 ) 2 ∫ x 3 ( π 2 ) 3 cos ⁡ ( t 1 3 ) …

Question

Verified Solution • 2025–26 Session moderate

QJEEM24Ma7ba7: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7ba7 Solution: lim x → π 2 ⁡ ( 1 ( x − π 2 ) 2 ∫ x 3 ( π 2 ) 3 cos ⁡ ( t 1 3 ) …

$lim_{x \to \frac{π}{2}} (\frac{1}{{(x - \frac{π}{2})}^{2}} \int_{x^{3}}^{{(\frac{π}{2})}^{3}} \cos (t^{\frac{1}{3}}) d t)$ is equal to

Multiple Choice Options

A 3π24
B 3π28
C 3π4
D 3π8

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Accepted Answer

Using L'hospital rule

$\begin{aligned} = lim_{x \to \frac{π^{-}}{2}} \frac{0 - \cos x \times 3 x^{2}}{2 (x - \frac{π}{2})} \\ = lim_{x \to \frac{π^{-}}{2}} \frac{\sin (x - \frac{π}{2})}{2 (x - \frac{π}{2})} \times \frac{3 π^{2}}{4} \\ = \frac{3 π^{2}}{8} \end{aligned}$

QJEEM24Ma7ba7: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7ba7 Solution: lim x → π 2 ⁡ ( 1 ( x − π 2 ) 2 ∫ x 3 ( π 2 ) 3 cos ⁡ ( t 1 3 ) …

Multiple Choice Options

Step-by-Step Verified Solution

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