Integral Calculus & Area · JEE Main previous year questions

2006 3 questions

1. Q232006 · 29 Apr 2006 · Shift 1

   The value of integral, ${\int }_3^6\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is

   1. A.$\frac{1}{2}$
   2. B.$\frac{3}{2}$
   3. C.2
   4. D.1
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   Answer: B

2. Q252006 · 29 Apr 2006 · Shift 1

   ${\int }_{-\frac{3\pi }{2}}^{-\frac{\pi }{2}}[(x+\pi {)}^3+{\cos }^2(x+3\pi )]dx$ is equal to

   1. A.$\frac{{\pi }^4}{32}$
   2. B.$\frac{{\pi }^4}{32}+\frac{\pi }{2}$
   3. C.$\frac{\pi }{2}$
   4. D.$\frac{\pi }{4}-1$
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   Answer: C

3. Q262006 · 29 Apr 2006 · Shift 1

   The value of ${\int }_1^a[x]f^{\prime }(x)dx,a>1$ where $[x]$ denotes the greatest integer not exceeding $x$ is

   1. A.$af(a)-\{f(1)+f(2)+\cdots +f([a])\}$
   2. B.$[a]f(a)-\{f(1)+f(2)+\cdots +f([a])\}$
   3. C.$[a]f([a])-\{f(1)+f(2)+\cdots +f(a)\}$
   4. D.$af([a])-\{f(1)+f(2)+\cdots +f(a)\}$
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   Answer: B