Mathematics

# Evaluate : $\int { \dfrac { 1-x }{ \sqrt { x } } } dx$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle\int { \dfrac { 1 }{ x\log { { x }^{ 2 } } } dx }$ is equal to
• A. $\log { \left| \log { { x }^{ 2 } } \right| } +C$
• B. $2\log { \left| \log { { x }^{ 2 } } \right| } +C$
• C. $4\log { \left| \log { { x }^{ 2 } } \right| } +C$
• D. $\dfrac { 1 }{ 4 } \log { \left| \log { { x }^{ 2 } } \right| } +C$
• E. $\dfrac { 1 }{ 2 } \log { \left| \log { { x }^{ 2 } } \right| } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Simplify: $\displaystyle \lim_{n\rightarrow \infty }\sum_{r=1}^{n}\frac{1}{n}e^{r/n}$
• A. e
• B. $\displaystyle 1-e$
• C. $\displaystyle e+1$
• D. $\displaystyle e-1$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral
$\int { \cfrac { { e }^{ x-1 }+{ x }^{ e-1 } }{ { e }^{ x }+{ x }^{ e } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find the value of $\displaystyle\int e^x(\tan x-\log|\cos x|)dx$

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 $\displaystyle f(x)>0 \forall x \in R$