Let $f(x)=\left\{\begin{array}{ll}\frac{1}{3}, & x \leq \frac{\pi} { 2} \ \frac{b(1-\sin x)}{(\pi-2 x)^2}, & x\frac{\pi} { 2}\end{array}\right.$ If $f$ is continuous at $x=\frac{\pi} { 2}$, then the value of $\int_0^{3 b-6}\left|x^2+2 x-3\right| d x$ is: [JEE Main 2026, 8 Apr (Shift 2)]

Question

Let $f(x)=\left\{\begin{array}{ll}\frac{1}{3}, & x \leq \frac{\pi} { 2} \ \frac{b(1-\sin x)}{(\pi-2 x)^2}, & x>\frac{\pi} { 2}\end{array}\right.$ If $f$ is continuous at $x=\frac{\pi} { 2}$, then the value of $\int_0^{3 b-6}\left|x^2+2 x-3\right| d x$ is: [JEE Main 2026, 8 Apr (Shift 2)]

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Let \(f(x)=\left\{\begin{array}{ll}\frac{1}{3}, & x \leq \frac{\pi} { 2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^2}, & x…

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Let \(f(x)=\left\{\begin{array}{ll}\frac{1}{3}, &amp; x \leq \frac{\pi} { 2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^2}, &amp; x…

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Let \(f(x)=\left\{\begin{array}{ll}\frac{1}{3}, & x \leq \frac{\pi} { 2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^2}, & x…