Mathematics

# Evaluate : $\int _ { \log 1 / 2 } ^ { \log 2 } \sin \left( \dfrac { e ^ { x } - 1 } { e ^ { x } + 1 } \right) d x$

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

#### Realted Questions

Q1 Subjective Hard
Evaluate the following integral:
$\displaystyle \int { \cfrac { 1 }{ x({ x }^{ n }+1) } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
Evaluate $\displaystyle \int_{-1}^{1}\log \frac{2-x}{2+x}dx.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate the following:
i) $\displaystyle\int { \dfrac { { x }^{ 2 } }{ \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+4 \right) } dx}$

ii) $\displaystyle \int { \dfrac { 1 }{ \cos ^{ 4 }{ x } +\sin ^{ 4 }{ x } } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int_{-\pi/2}^{\pi/2} (sin^3x+cos^3x)dx$ equals-
• A. $0$
• B. $1/3$
• C. $2/3$
• D. $4/3$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020