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MathsJEE Main 8 Apr 2026, Shift 2·Q19·MCQ·Moderate

Definite Integration · Integral of modulus function

Let f(x)={13,x≤π2b(1−sin⁡x)(π−2x)2,x>π2,f(x) = \begin{cases} \dfrac13, & x \le \dfrac{\pi}{2}\\[2ex] \dfrac{b(1 - \sin x)}{(\pi - 2x)^2}, & x > \dfrac{\pi}{2}\end{cases}, If ff is continuous at x=π/2x = \pi/2, then the value of ∫03b−6∣x2+2x−3∣dx\displaystyle\int_0^{3b-6}\left\lvert x^2 + 2x - 3\right\rvert dx is:
  1. (1)5
  2. (2)2
  3. (3)3
  4. (4)4

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