Mathematics

# $\displaystyle \int_2^3\dfrac{dx}{x^2-1}$

$\dfrac{1}{2}log\dfrac{3}{2}$

##### SOLUTION
$\int _{ 2 }^{ 3 }{ \frac { dx }{ { x }^{ 2 }-1 } } \\ \int _{ 2 }^{ 3 }{ \frac { dx }{ (x-1)(x+1) } } \\ \frac { 1 }{ 2 } \int _{ 2 }^{ 3 }{ \frac { 1 }{ x-1 } } -\frac { 1 }{ x+1 } \\ =\frac { 1 }{ 2 } \int _{ 2 }^{ 3 }{ \ln { (x-1) } -\ln { (x+1) } } \\ =\frac { 1 }{ 2 } \ln { \frac { 3 }{ 2 } }$
Option $D$ is correct.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Medium
Solve:
$\int_{1}^{2}\dfrac{ \sqrt {x} }{ {\sqrt{3 - x} + \sqrt{x}}}dx$.

• A. $\dfrac 14$
• B. $1$
• C. None of these
• D. $\dfrac 12$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\int \dfrac {1}{\sqrt {\sin^{3}x \cos^{5}x}} dx$ is
• A. $\dfrac {2}{\sqrt {\tan x}} - \dfrac {2}{3} (\tan x)^{3/2} + C$
• B. $\dfrac {-2}{\sqrt {\tan x}} + \dfrac {2}{3} (\tan x)^{1/2} + C$
• C. None of these
• D. $\dfrac {-2}{\sqrt {\tan x}} + \dfrac {2}{3} (\tan x)^{3/2} + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\mathrm{If } \lambda=\int_{0}^{1} \dfrac{e^{t}}{1+t},$ then $\int_{0}^{1} e^{t} \log _{e}(1+t) d t$ is equal to
• A. $2 \lambda$
• B. $\lambda$
• C. $e \log _{e} 2+\lambda$
• D. $e \log _{e} 2-\lambda$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate $\int _{ 0 }^{ 5 }{ (x+1)dx }$ as limit of sum

1 Verified Answer | Published on 17th 09, 2020

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 $(0, 1)$