Mathematics

The value of${\smallint _{100}}{1000}\frac{{dx}}{x}is$

$4.606$

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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 Hard
If $\displaystyle\int \frac{dx}{\sqrt{\sin^{3} x\cos^{5} x}}=a\sqrt{\cot x}+b\sqrt{\tan^{3} x}+C$, then

• A. $a = -1,\>b = \displaystyle \frac {1}{3}$
• B. $a = -3,\>b = \displaystyle \frac {2}{3}$
• C. $a = -2,\>b = \displaystyle \frac {4}{3}$
• D. $a = -2,\>b = \displaystyle \frac {2}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Hard
If $\displaystyle I=\int \frac{\sin x\left ( \cos x \right )^{-5/2}dx}{\sqrt{\sin x+3\cos x}+\sqrt{\sin x+4\cos x}}$$\displaystyle= \frac { A }{ 1550 } \left( \left( \tan x+4 \right) ^{ 5/2 }-\left( \tan x+3 \right) ^{ 3/2 } \right) -\frac { 2 }{ 3 } \left[ 4\left( \tan x+4 \right) ^{ 3/2 }-3{ \left( \tan { x } +3 \right) }^{ 3/2 } \right] +C$,
then the value of A is equal to

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle\int^1_0\dfrac{dx}{\sqrt{1-x^2}}$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\displaystyle\int \log \left( {\log x} \right) + {\left( {\log x} \right)^{ - 2}}= ?$

$I=\displaystyle \int{\dfrac{1}{\sqrt{21+4x-4x^{2}}}dx}$