Mathematics

# Evaluate the following integrals:$\displaystyle \int { \cfrac { 1 }{ \sqrt { 16-6x-{ x }^{ 2 } } } } dx$

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

#### Realted Questions

Q1 Single Correct Hard
Evaluate $\displaystyle\int{\sqrt{x+\sqrt{x^2+2}}dx}$.
• A. $\displaystyle\frac{1}{3}{(x+\sqrt{x^2+2})}^{\tfrac{1}{2}}+2\frac{1}{\sqrt{x+\sqrt{x^2+2}}}+C$
• B. $\displaystyle\frac{2}{3}{(x+\sqrt{x^2+2})}^{\tfrac{2}{3}}+2\frac{1}{\sqrt{x+\sqrt{x^2+2}}}+C$
• C. None of these
• D. $\displaystyle\frac{1}{3}{(x+\sqrt{x^2+2})}^{\tfrac{3}{2}}-2\frac{1}{\sqrt{x+\sqrt{x^2+2}}}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int x^{3}[\frac{1-\sin(4\log x)}{1-cos(4\log x)}]dx=$
• A. $x^{4}$ cot $(2 \log x)+c$
• B. $\displaystyle e^{4x}\frac{1}{1-cos(4\log x)}+c$
• C. $\displaystyle \frac{x^4}{4}cot(2logx)+c$
• D. $\displaystyle \frac{-x^{4}}{4}cot(2\log x)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \dfrac {dx}{\sin x. \sin (x + a)}$ is equal to
• A. $cosec \, a \, ln \left |\dfrac {\sin (x + a)}{\sin x}\right | + C$
• B. $cosec \, a \, ln \left |\dfrac {\sin (x + a)}{\sec x}\right | + C$
• C. $cosec \, a \, ln \left |\dfrac {\sec x}{\sec (x + a)}\right | + C$
• D. $cosec \, a \, ln \left |\dfrac {\sin x}{\sin (x + a)}\right | + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle \frac{x^3-6x^2+10x-2}{x^2-5x+6}=f(x)+\frac{A}{x-2}+\frac{B}{x-3}$, then $f(x)=$
(Note : $A,B$ are constants)
• A. $x+1$
• B. $x$
• C. $x+2$
• D. $x-1$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$