Mathematics

# Evaluate $\displaystyle \int { \dfrac { 1-4x }{ \sqrt { 6+x-{ 2x }^{ 2 } } } } dx$

##### SOLUTION
Let $t=6+x-2x^2\\dt=1-4x dx$

$\displaystyle \int \dfrac 1{\sqrt t} dt\\2\sqrt t+c\\2\sqrt{6+x-2x^2}+c$

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

#### Realted Questions

Q1 Single Correct Medium
If $f(a+b-x)=f(x)$ then $\int _{a}^{b}{x\ f(x)dx}=$

• A. $\int _{ a }^{ b }{ f\left( x \right) dx }$
• B. $(a+b)\int _{ a }^{ b }{ f\left( x \right) dx }$
• C. $0$
• D. $\left( \dfrac { a+b }{ 2 } \right) \int _{ a }^{ b }{ f\left( x \right) dx }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int e^{2x} (\sqrt{3}cosx-sinx)dx=$
• A. $\displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)cosx -(\sqrt{3}-2)sinx]+c$
• B. $\displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)sinx+(\sqrt{3}-2)\cos x]+c$
• C. $\displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)sinx-(\sqrt{3}-2)cosx]+c$
• D. $\displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)cosx+(\sqrt{3}-2)sin x]+c$

1 Verified Answer | Published on 17th 09, 2020

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$\int \sin^{-1}\left(\dfrac {2x}{1+x^{2}}\right)dx=f(x)-\log(1+x^{2})+c \Rightarrow f(x)=$
• A. $-2x\ \tan^{-1}x$
• B. $x\ \tan^{-1}x$
• C. $-x\ \tan^{-1}x$
• D. $2x\ \tan^{-1}x$

1 Verified Answer | Published on 17th 09, 2020

Q4 TRUE/FALSE Medium
$\int \sqrt {x^2 + a^2} dx =\dfrac{x}{2} \sqrt {x^2 + a^2} + \dfrac{a^2}{2} log (x +\sqrt {x^2 + a^2)} +c$
• A. False
• B. True

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int _{ 1 }^{ 3 }{ \log { x } } dx=......\left( x>0\in { R }^{ + } \right)$
• A. $-2+\log { 9 } \quad$
• B. $2+\log { 27 }$
• C. $\log { \left( \cfrac { 27 }{ e } \right) }$
• D. $-2+\log { 27 }$