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Subjects 9
Chapters 126
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Realted Questions

Q1 Single Correct Hard
$$\displaystyle \int { \cfrac { { x }^{ 3 } }{ \sqrt { 1+x^2 }  }  } dx$$
  • A. $$\sqrt { 1+x } -\cfrac { x }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$$
  • B. $$x\sqrt { 1+{ x }^{ 2 } } +\cfrac { 2 }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$$
  • C. $${ x }^{ 2 }\sqrt { 1+{ x }^{ 2 } } -\cfrac { 1 }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$$
  • D. $$\dfrac{{ x }^{ 2 }\sqrt { 1+{ x }^{ 2 } }}{3}-\cfrac { 2 }{ 3 } {\sqrt{1+{ x }^{ 2 }} }+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
Integrate:
$$\frac { 3 x + 5 } { ( x + 1 ) ( x - 2 ) ^ { 2 } } d x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
What is $$\displaystyle \int { \cfrac { \ln { x }  }{ x }  } dx$$ equal to ?
  • A. $$\cfrac { \left( \ln { x } \right) }{ 2 } +c$$ where $$c$$ is the constant of integration
  • B. $${ \left( \ln { x } \right) }^{ 2 }+c$$ where $$c$$ is the constant of integration
  • C. None of the above
  • D. $$\cfrac { { \left( \ln { x } \right) }^{ 2 } }{ 2 } +c$$ where $$c$$ is the constant of integration

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
If $$\displaystyle \int \dfrac{x^4 + 1}{x^6 + 1} dx = \tan^{-1} (f(x)) -\dfrac{2}{3} \tan^{-1} (g(x)) + C$$, then
  • A. $$g(x)$$ is monotonic function
  • B. none of these
  • C. None 
  • D. Both $$f(x)$$ & $$g(x)$$ are odd functions

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

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