Mathematics

# If  $I _ { 1 } = \int _ { 0 } ^ { 1 } 2 ^ { x ^ { 2 } } d x , I _ { 2 } = \int _ { 0 } ^ { 1 } 2 ^ { x ^ { 3 } } d x , I _ { 3 } = \int _ { 1 } ^ { 2 } 2 ^ { x ^ { 2 } } d x$ and $I _ { 4 } = \int _ { 1 } ^ { 2 } 2 ^ { x ^ { 3 } } d x$  then

$\mathrm { l } _ { 3 } > \mathrm { I } _ { 4 }$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int\frac{d_{X}}{\sin^{2}x+\sin2x}=$
• A. $\displaystyle \frac{-1}{2}\log|\frac{\tan x}{\tan x+2}|+c$
• B. $\displaystyle \frac{1}{3}\log|\displaystyle \frac{\tan x}{\tan x+2}|+c$
• C. $\displaystyle -\frac{1}{3}\log|\displaystyle \frac{\tan x}{\tan x+2}|+c$
• D. $\displaystyle \frac{1}{2}\log|\displaystyle \frac{\tan x}{\tan x+2}|+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
The value of integral $\int _{ \cfrac { \pi }{ 4 } }^{ \cfrac { 3\pi }{ 4 } }{ \cfrac { x }{ 1+\sin { x } } } dx$ is

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle\int^{\frac{3}{2}}_{-1}|x\sin(\pi x)|dx$.
• A. $3\pi +\pi^2$
• B. $\dfrac { 2 }{ \pi } +\dfrac { 1 }{ { \pi }^{ 2 } }$
• C. none of the above
• D. $\dfrac {3}{\pi} +\dfrac {1}{\pi^2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 TRUE/FALSE Medium
State true or false:
The average value of the function $f(x) = sin^2xcos^3x$ on the interval $[ -\pi ,\pi ]$ is 0.
• A. False
• B. True

$\int \frac{2x^{2}}{3x^{4}2x} dx$