Mathematics

# The value of  $\int _{ { \sqrt { \ln { 2 } } } }^{ { \sqrt { \ln { 3 } } } } \dfrac { x\sin x^{ { 2 } } }{ \sin x^{ { 2 } }+\sin \left( \ln { 6 } -x^{ { 2 } } \right) } dx$  is

$\dfrac { 1 } { 4 } \ln \dfrac { 3 } { 2 }$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^{\pi/4}_0\dfrac{\tan^3x}{(1+\cos 2x)}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

Statement- 1 :$\lim_{n\rightarrow \infty }\dfrac{1^{m}+2^{m}+3^{m}+....n^{m}}{n^{m+1}}=\dfrac{1}{m+1}(m\neq -1)$

##### REASON

Statement- 2 : The above limit equals $\int_{0}^{1}x^{m}dx$

• A. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1
• B. Statement -1 is True, Statement -2 is False
• C. Statement -1 is False, Statement -2 is True
• D. Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The anti derivative of $\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)$ equals
• A. $\dfrac{1}{3}x^{\dfrac{1}{3}}+2x^{\dfrac{1}{2}}+C$
• B. $\dfrac{2}{3}x^{\dfrac{2}{3}}+\dfrac{1}{2}x^{2}+C$
• C. $\dfrac{2}{3}x^{\dfrac{3}{2}}+\dfrac{1}{2}x^{\dfrac{1}{2}}+C$
• D. $\dfrac{2}{3}x^{\dfrac{3}{2}}+2x^{\dfrac{1}{2}}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int \frac{1}{x\sqrt{1-x^{3}}}dx=a\log \left | \frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1} \right |+b$, then a is equal to
• A. $\displaystyle\frac {2}{3}$
• B. $\displaystyle \frac {-1}{3}$
• C. $\displaystyle \frac {-2}{3}$
• D. $\displaystyle\frac {1}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int {\cfrac{{dx}}{{{x^2}{{\left( {1 + {x^5}} \right)}^{4/5}}}}}$ is equal to:
• A. $- \cfrac{{{{\left( {1 + {x^5}} \right)}^{1/5}}}}{{5x}} + {\rm{C}}$
• B. $\cfrac{{{{\left( {1 + {x^5}} \right)}^{1/5}}}}{{5x}} + {\rm{C}}$
• C. $\cfrac{{{{\left( {1 + {x^5}} \right)}^{1/5}}}}{x} + {\rm{C}}$
• D. $- \cfrac{{{{\left( {1 + {x^5}} \right)}^{1/5}}}}{x} + {\rm{C}}$