Mathematics

# Evaluate the following integrals$\int { \cfrac { 2\sin { x } +3\cos { x } }{ 3\sin { x } +4\cos { x } } } dx\quad$

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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 Medium
The value of intergral $\displaystyle \int_{\dfrac{\pi}{4}}^{\dfrac{3\pi}{4}}\dfrac{x}{1+\sin x}dx$ is :
• A. $\pi\sqrt{2}$
• B. $\dfrac{\pi}{2}(\sqrt{2}+1)$
• C. $2\pi (\sqrt{2}-1)$
• D. $\pi(\sqrt{2}-1)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
The value of $\int _{ 0 }^{ { \pi }/{ 2 } }{ \cfrac { dx }{ 1+\tan ^{ 3 }{ x } } }$ is

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle \int \dfrac {5x^{4}+4x^{5}}{(x^{5}+x+1)^{2}}dx=f(x)+c$, then $f(x)=$
• A. $\dfrac {x^{4}+x^{5}}{x^{5}+x+1}$
• B. $\dfrac {x^{5}}{x^{6}+x^{2}+x}$
• C. $none\ of\ these$
• D. $\dfrac {x^{5}}{x^{5}+x+1}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals:
$\displaystyle \int { \cfrac { 1 }{ { x }^{ 2/3 }\sqrt { { x }^{ 2/3 }-4 } } } dx\quad$

Solve$\displaystyle \int_0^1 \dfrac{x^2-2}{x^2+1}dx$