JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Definite Integrals

More JEE Advanced questions on Definite Integrals

1. If
   

   $$\alpha ={\int }_{\frac{1}{2}}^2\frac{{\tan }^{-1}x}{2x^2-3x+2}dx$$

   
   then the value of $\sqrt{7}\tan \left(\frac{2\alpha \sqrt{7}}{\pi }\right)$ is ____.
   (Here, the inverse trigonometric function ${\tan }^{-1}x$ assumes values in …
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2. Let the function $f:[1,\infty )\to \mathbb{R}$ be defined by …
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3. Let $f:\left[0,\frac{\pi }{2}\right]\to [0,1]$ be the function defined by $f(x)={\sin }^{2}x$ and let $g:\left[0,\frac{\pi }{2}\right]\to [0,\infty )$ be the function defined by $g(x)=\sqrt{\frac{\pi x}{2}-x^2}$.
   
   The value of …
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4. Let $f:\left[0,\frac{\pi }{2}\right]\to [0,1]$ be the function defined by $f(x)={\sin }^{2}x$ and let $g:\left[0,\frac{\pi }{2}\right]\to [0,\infty )$ be the function defined by $g(x)=\sqrt{\frac{\pi x}{2}-x^2}$.
   
   The value of …
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5. For $\mathrm{x}\in \mathbb{R}$, let ${\tan }^{-1}(\mathrm{x})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$. Then the minimum value of the function $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ defined by …
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6. Consider the equation
   

   $${\int }_1^e\frac{{\left({\log }_{e}x\right)}^{1/2}}{x{\left(a-{\left({\log }_{e}x\right)}^{3/2}\right)}^2}dx=1,a\in (-\infty ,0)\cup (1,\infty ).$$

   
   Which of the following statements is/are TRUE ?
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