Mathematics

Evaluate:
$$\displaystyle \int{\dfrac{x^{4}}{(x-1)(x^{2}+1)}dx}$$


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Subjective Medium Published on 17th 09, 2020
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Realted Questions

Q1 Single Correct Medium
$$\int \dfrac{x}{\sqrt{x^2+2}}dx$$
  • A. $$\dfrac{x^2+2}{2}+C$$
  • B. $$x^2+2+C$$
  • C. $$\dfrac{1}{2}\sqrt{x^2+2}+C$$
  • D. $$\sqrt{x^2+2}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
If f(x) be an increasing function defined on [a, b] then
max {f(t) such that $$a\leq t\leq x$$, $$a\leq x\leq b$$}=f(x)  & min {f(t), $$a\leq t\leq x$$, $$a\leq x\leq b$$}=f(a) and if f(x) be decreasing function defined on [a, b] then
max {f(t), $$a\leq t\leq x$$, $$a\leq x\leq b$$}=f(a),
min {f(t), $$a\leq t\leq x$$, $$a\leq x\leq b$$}=f(x).
On the basis of above information answer the following questions.

Let $$f\left ( x \right )=min. \left \{ \left | x \right |, \left | x-1 \right |, \left | x+1 \right | \right \}$$ then $$\int_{-1}^{1}f\left ( x \right )dx$$ equals
  • A. $$\displaystyle \frac{1}{4}$$
  • B. 1
  • C. None of these
  • D. $$\displaystyle \frac{1}{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Hard
$$I=\displaystyle \int x^{3}\log{x}\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Integrate: $$f(x)=\dfrac { \sin ^{ 3 }{ x } +\cos ^{ 3 }{ x }  }{ \sin ^{ 2 }{ x } \cos ^{ 2 }{ x }  }$$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Hard
The value of $$\underset {n\rightarrow \infty}{\lim}\dfrac {1}{n}\displaystyle \sum_{r = 1}^{r = 2n} \dfrac {r}{\sqrt {n^{2} + r^{2}}}$$ equals.
  • A. $$\sqrt {5} + 1$$
  • B. $$1 = \sqrt {5}$$
  • C. None of these
  • D. $$\sqrt {5} - 1$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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