Integral Calculus & Area · JEE Main previous year questions

2015 3 questions

1. Q122015 · 4 Apr 2015 · Shift 1

   The integral $\int \frac{dx}{x^2(x^4+1{)}^{3/4}}$ equals :

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

2. Q132015 · 4 Apr 2015 · Shift 1

   The integral ${\int }_2^4\frac{\log x^2}{\log x^2+\log (36-12x+x^2)}dx$ is equal to :

   1. A.$1$
   2. B.$6$
   3. C.$2$
   4. D.$4$
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   Answer: A

3. Q142015 · 4 Apr 2015 · Shift 1

   The area (in sq. units) of the region described by $\left\{(x,y):y^2\le 2x\text{ and }y\ge 4x-1\right\}$ is :

   1. A.$\frac{15}{64}$
   2. B.$\frac{9}{32}$
   3. C.$\frac{7}{32}$
   4. D.$\frac{5}{64}$
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   Answer: B