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Q.64 lim x→π/2 { 1/(x−π/2)^2 ∫[x^3 to (π/2)^3] cos(t^(1/3)) dt } is equal to-
- 3π/4
- 3π/8
- 3π^2/4
- 3π^2/8
Correct answer: 3π^2/8
Solution
The limit evaluates the behavior of the integral as x approaches π/2, where the integral's upper limit approaches a constant value and the denominator approaches zero, leading to a specific finite limit that simplifies to 3π^2/8.
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