Mathematics

# Let $I_1=\displaystyle\int^1_0\dfrac{e^xdx}{1+x}$ and $I_2=\displaystyle\int^1_0\dfrac{x^2dx}{e^{x^3}(2-x^3)}$, then $\dfrac{I_1}{I_2}$ is?

$3/e$

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

#### Realted Questions

Q1 Single Correct Medium
The correct evaluation of $\displaystyle \int _ { 0 } ^ { \pi / 2 } \sin x \sin 2 x$ is
• A. $\dfrac { 4 } { 3 }$
• B. $\dfrac { 1 } { 3 }$
• C. $\dfrac { 3 } { 4 }$
• D. $\dfrac { 2 } { 3 }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int \sqrt {2x+5}dx$
• A. $\dfrac 1{\sqrt {2x+5}}$
• B. $\dfrac{3}{5}(2x+5)^{3/5}$
• C. $\dfrac 1{2x+5}$
• D. $\dfrac 13(2x+5)^{3/2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int\frac{\log(x+1)-\log x}{x(x+1)}dx=$
• A. $\displaystyle \log(x-1)\log x+\frac{1}{2}(\log(x-1))^{2}-\frac{1}{2}(\log x)^{2}+c$
• B. $\displaystyle \frac{1}{2}(\log(x+1))^{2}+\frac{1}{2}(\log x)^{2}-\log(x+1)\log x+c$
• C. $[(\displaystyle \log(1+\frac{1}{x})]^{2}+c$
• D. $-\displaystyle \frac{1}{2}[\log (1+\displaystyle \frac{1}{x})]^{2}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve $\int {r^5} {e^x} dx$:
(Given $r$ is constant)

$\displaystyle \int_0^{\frac{\pi}{4}} {\cfrac{{{{\cos }^4}x - {{\sin }^4}x}}{{\sqrt {1 + \sin 2x} }}dx} =\sqrt 2$