Mathematics

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

Q1 Subjective Hard
Evaluate : $$\int^1_0$$$$\frac{log (1 +x)}{1 + x^2}dx$$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
If $$\displaystyle \int \frac{dx}{\left ( x-p \right )\sqrt{\left ( x-p \right )\left ( x-q \right )}} \displaystyle =-\frac{2}{p-q}\sqrt{\frac{x-a}{x-b}}+c$$ then find $$a$$ and $$b$$ are respectively
  • A. $$p,q$$
  • B. $$q,q^2$$
  • C. $$p^2,q^2$$
  • D. $$q,p$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
$$\text { Evaluate: } \displaystyle \int e^{x}\left(\dfrac{\sin 4 x-4}{1-\cos 4 x}\right) d x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium

$$\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{f(\sin x)}{f(\sin x)+f(\cos x)}dx=$$
  • A. $$\pi$$
  • B. $$2\pi$$
  • C. $$\dfrac {\pi}{2}$$
  • D. $$\dfrac {\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Hard
Given that for each $$\displaystyle a  \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$$ exists. Let this limit be $$g(a)$$ 
In addition, it is given that the function $$g(a)$$ is differentiable on $$(0, 1)$$
Then answer the following question.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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