Integral Calculus & Area · JEE Main previous year questions

2016 2 questions

1. Q112016 · 3 Apr 2016 · Shift 1

   The integral $\int \frac{2x^{12}+5x^9}{(x^5+x^3+1{)}^3}dx$ is equal to :

   1. A.$-\frac{x^5}{2(x^5+x^3+1{)}^2}+C$
   2. B.$\frac{-x^{10}}{2(x^5+x^3+1{)}^2}+C$
   3. C.$\frac{-x^5}{(x^5+x^3+1{)}^2}+C$
   4. D.$\frac{x^{10}}{2(x^5+x^3+1{)}^2}+C$
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   Answer: D

2. Q122016 · 3 Apr 2016 · Shift 1

   The area (in sq. units) of the region $\left\{(x,y):y^2\ge 2x\text{ and }{x}^2+y^2\le 4x,x\ge 0,y\ge 0\right\}$ is :

   1. A.$\pi -\frac{4\sqrt{2}}{3}$
   2. B.$\frac{\pi }{2}-\frac{2\sqrt{2}}{3}$
   3. C.$\pi -\frac{4}{3}$
   4. D.$\pi -\frac{8}{3}$
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   Answer: D