Mathematics

Single Correct Medium Published on 17th 09, 2020
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Realted Questions

Q1 Subjective Medium
$$\displaystyle\int_{0}^{1} x^2-3x \  dx $$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Evaluate: $$\displaystyle \int \sqrt{x^{2}-x+1}dx.$$
  • A. $$\displaystyle\frac{2x+1}{4}\sqrt{x^{2}-x+1}+\frac{3}{8}\log \left \{ \frac{2x+1}{2}+\sqrt{x^{2}-x+1} \right \}$$
  • B. $$\displaystyle\frac{2x+1}{2}\sqrt{x^{2}-x+1}+\frac{3}{8}\log \left \{ \frac{2x-1}{4}+\sqrt{x^{2}-x+1} \right \}$$
  • C. $$\displaystyle\frac{2x-1}{3}\sqrt{x^{2}-x+1}-\log \left \{ \frac{2x-1}{2}+\sqrt{x^{2}-x+1} \right \}$$
  • D. $$\displaystyle\frac{2x-1}{3}\sqrt{x^{2}-x+1}+\frac{3}{8}\log \left \{ \frac{2x-1}{2}+\sqrt{x^{2}-x+1} \right \}$$
  • E. $$\displaystyle\frac{2x-1}{2}\sqrt{x^{2}-x+1}+\frac{3}{8}\log \left \{ \frac{2x-1}{4}+\sqrt{x^{2}-x+1} \right \}$$
  • F. $$\displaystyle\frac{2x-1}{4}\sqrt{x^{2}-x+1}-\frac{3}{8}\log \left \{ \frac{2x-1}{2}+\sqrt{x^{2}-x+1} \right \}$$
  • G. $$\displaystyle\frac{2x-1}{4}\sqrt{x^{2}-x+1}+\frac{3}{8}\log \left \{ \frac{2x-1}{2}+\sqrt{x^{2}-x+1} \right \}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Hard
Evaluate: $$\displaystyle {\int {\left( {\dfrac{{1 - x}}{{1 + {x^2}}}} \right)} ^2}{e^x}\,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
$$\displaystyle \int _{ 0 }^{ a }{ \frac { dx }{ a+\sqrt { { a }^{ 2 }-{ x }^{ 2 } }  }  } $$ is equal to
  • A. $$\displaystyle \frac { \pi  }{ 2 } +1$$
  • B. $$\displaystyle 1-\frac { \pi  }{ 2 } $$
  • C. none of these
  • D. $$\displaystyle \frac { \pi  }{ 2 } -1$$

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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