Mathematics

# Let $A = \int\limits_0^1 {\cfrac{{{e^t}}}{{1 + t}}dt}$, then $\int\limits_{a - 1}^a {\cfrac{{{e^{ - t}}}}{{t - a - 1}}dt}$ has the value

$- A{e^{ - a}}$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle\int^{\lambda}_0\dfrac{y}{\sqrt{y+\lambda}}dy=?$
• A. $\dfrac{2}{3}(2+\sqrt{2})\lambda\sqrt{\lambda}$
• B. $\dfrac{1}{3}(2-\sqrt{2})\lambda \sqrt{\lambda}$
• C. $\dfrac{1}{3}(2+\sqrt{2})\lambda \sqrt{\lambda}$
• D. $\dfrac{2}{3}(2-\sqrt{2})\lambda \sqrt{\lambda}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate $\displaystyle\int \dfrac {6x}{3x^2+8}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate the given integral.
$\displaystyle\int { \cfrac { \sin ^{ 2 }{ x } }{ \cos ^{ 4 }{ x } } } dx$
• A. $\cfrac { 1 }{ 3 } \tan ^{ 2 }{ x } +C\quad \quad$
• B. $\cfrac { 1 }{ 2 } \tan ^{ 2 }{ x } +C\quad$
• C. None of these
• D. $\cfrac { 1 }{ 3 } \tan ^{ 3 }{ x } +C\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{1+x^{5}}{1+x}dx$ is equal to
• A. $1-x+x^{2}-x^{3}+x^{4}+c$
• B. $(1+x)^{5}+c$
• C. $(1-x)^{5}+c$
• D. $x-\displaystyle \frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\frac{x^{5}}{5}+c$

$\displaystyle \int { \dfrac { dx }{ \tan { x } +\cot { x } } = }$