Mathematics

# If $I_{1}=\displaystyle \int_{e}^{e^{2}}\dfrac{dx}{\ell n x}$ and $I_{2}=\int_{1}^{2} \dfrac{e^{x}}{x}dx$, then

$I_{1}=I_{2}$

##### SOLUTION

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 Subjective Medium
By using the properties of definite integrals, Show that $\displaystyle \int_0^a f(x) g (x) dx=2\int_0^af(x)dx$, if $f$ and $g$ are defined as $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integerate:
$\int {x\,\cos \,x\,dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If a curve passes through the point $\left( 2,\cfrac { 7 }{ 2 } \right)$ and has slope $\left( 1-\cfrac { 1 }{ { x }^{ 2 } } \right)$ at any point $(x,y)$ on it, then the ordinate of the point on the curve whose abscissa is $-2$ is:
• A. $-\cfrac { 5 }{ 2 }$
• B. $\cfrac { 3 }{ 2 }$
• C. $\cfrac { 5 }{ 2 }$
• D. $-\cfrac { 3 }{ 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int_{0}^{1}\frac{d}{dx}$ $tan^{-1} \left( \displaystyle \frac { 1 }{ x } \right)$

• A. $\dfrac{\pi}{4}$
• B. $\dfrac{-\pi}{2}$
• C. $\dfrac{\pi}{2}$
• D. $\dfrac{-\pi}{4}$

If $\displaystyle \int \dfrac{e^x - 1}{e^x + 1}dx =f(x) + c$ then $f(x) =$