Mathematics

# What is the value of $\int_{0}^{\pi}\dfrac {dx}{5-4\cos x}$?

$\dfrac {\pi \log 2}{32}$

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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
The value of $\displaystyle \int { { e }^{ x }\frac { 1+n{ x }^{ n-1 }-{ x }^{ 2n } }{ \left( 1-{ x }^{ n } \right) \sqrt { 1-{ x }^{ 2n } } } dx }$ is
• A. $\displaystyle { e }^{ x }\frac { \sqrt { 1-{ x }^{ n } } }{ 1-{ x }^{ n } } +c$
• B. $\displaystyle { e }^{ x }\frac { \sqrt { 1+{ x }^{ 2n } } }{ 1-{ x }^{ 2n } } +c$
• C. $\displaystyle { e }^{ x }\frac { \sqrt { 1-{ x }^{ 2n } } }{ 1-{ x }^{ 2n } } +c$
• D. $\displaystyle { e }^{ x }\frac { \sqrt { 1-{ x }^{ 2n } } }{ 1-{ x }^{ n } } +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int_{-2}^{0}\left \{ x^{3}+3x^{2}+3x+3+(x+1)cos(x+1) \right \}dx$ is
• A. $-4$
• B. $0$
• C. $6$
• D. $4$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int {\frac{{{{\sin }^{ - 1}}x}}{{{{\left( {1 - {x^2}} \right)}^{\frac{3}{2}}}}}dx}$
• A. $\frac{1}{2}\log \left| {\left( {1 - {x^2}} \right)} \right| + C$
• B. $\frac{{x\left( {{{\sin }^{ - 1}}x} \right)}}{{\sqrt {1 - {x^2}} }}+C$
• C. $4+\frac { \pi }{ 2 }$
• D. $\frac{{x\left( {{{\sin }^{ - 1}}x} \right)}}{{\sqrt {1 - {x^2}} }} + \frac{1}{2}\log \left| {\left( {1 - {x^2}} \right)} \right| + C.$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\int {\dfrac{{{\text{ln}}\left( {{\text{e}}{{\text{x}}^{\text{x}}}} \right)}}{{{\text{x}}{{\text{e}}^{\text{x}}}{{\left( {{\text{lnx}}} \right)}^{\text{2}}}}}} {\text{dx}}\;{\text{is}}$
• A. $\dfrac{{\text{1}}}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$
• B. $\dfrac{{{e^2}}}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$
• C. $- \dfrac{1}{{{{\text{e}}^{{\text{ - x}}}}{\text{lnx}}}}{\text{ + c}}$
• D. $- \dfrac{1}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$