Mathematics

# If $I=\displaystyle\int _{ 8 }^{ 15 }{ \dfrac { dx }{ \left( x-3 \right) \sqrt { x+1 } } }$, then $I$ equals

$\dfrac{1}{2}\log\dfrac{5}{3}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
$\int \dfrac {dx}{(x - 1)\sqrt {x^{2} - 1}} =$
(c is a constant)
• A. $-\sqrt {\dfrac {x - 1}{x + 1}} + C$
• B. $\sqrt {\dfrac {x - 1}{x^{2} + 1}} + C$
• C. $\sqrt {\dfrac {x^{2} + 1}{x - 1}} + C$
• D. $-\sqrt {\dfrac {x + 1}{x - 1}} + C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following definite integral:
$\displaystyle \int _{\pi /6}^{\pi /4} \csc x \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \underset{0}{\overset{x}{\int}} \dfrac{(t - |t|)^2}{(1 + t^2)} dt$ is equal to
• A. $0 \, if \, x > 0$
• B. $\ln ( 1 + x^3) \, \ \text{if} \, x > 0$
• C. $4(x + \tan^{-1} x ) \, \text{if} \, x < 0$
• D. $4(x - \tan^{-1} x), \, \ \text{if} \, x < 0$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\int\limits_0^\pi {\cos }(2x)$.$\log\sin x\;dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int { (\cfrac { { 2 }^{ x }-5^{ x } }{ 10^{ x } } )dx }$ is equal to __________________.
• A. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• B. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } +\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• C. $\cfrac { { 5 }^{ -x } }{ \log _{ e }{ 5 } } -\cfrac { 2^{ -x } }{ \log _{ e }{ 2 } } +c$
• D. $\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$