Mathematics

# $if\,{l_n} = \int\limits_0^1 {{x^m}} {\left( {\ln x} \right)^n}dx,\,and\,{l_n} = \frac{1}{{m + 1}}{l_{n - 1}}.then\,is$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate :
$\displaystyle \int \dfrac{8^{1+x}+4^{1-x}}{2^x}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If  $\int x ^ { 2 } \cdot e ^ { - 2 x } d x = e ^ { - 2 x } \left( a x ^ { 2 } + b x + c \right) + d,$  then
• A. $a = 1 , b = 1 , c = \dfrac { 1 } { 2 }$
• B. $a = 1 , b = - 1 , c = - \dfrac { 1 } { 2 }$
• C. $a = 1 , b = 1 , c = - \dfrac { 1 } { 2 }$
• D. None of these

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int { \dfrac { \cos { x } }{ 1-\cos { x } } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { \cfrac { 2x+5 }{ \sqrt { { x }^{ 2 }+2x+5 } } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$

Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020