Mathematics

# If $y(x-y)^{2}=x$ then $\displaystyle\int { \cfrac { 1 }{ x-3y } dx }$ is

$\dfrac{1}{3}\ln { \left( 1+{ \left( x-y \right) }^{ 2 } \right) }$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the given integral.
$\int { x\cos { x } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Let $y=f(x)$ be a continuous function such that $(3-x)=f(3+x)\ \forall\ x\ \in\ R$. If $\displaystyle \int^{-2}_{-5}f(x)dx=2\int^{2}_{-2}f(x)dx=3$ and $\displaystyle \int^{4}_{2}f(x)dx=4$ then the value of $\displaystyle \int^{11}_{-5}f(x)dx$ equals
• A. $16$
• B. $14$
• C. $12$
• D. $18$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:

$\displaystyle\int_{0}^{\pi/2}\dfrac{\sin x+\cos x}{3+\sin 2x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle I = \int \cot^{-1} \left ( \frac {a^2 - ax + x^2}{a^2} \right ) dx$, then $I$ equals
• A. $\displaystyle x \tan^{-1} \left ( \frac {x}{a} \right ) - (x - a) \tan^{-1} \left ( \frac {x - a}{a} \right ) + C$
• B. $\displaystyle \frac {a}{2} \log (2a^2 - 2ax + x^2) - \frac {a}{2} \log (x^2 + a^2) + C$
• C. $\displaystyle x \tan^{-1} \left ( \frac {x}{a} \right ) + (x - a) \tan^{-1} \left ( \frac {x - a}{a} \right ) + \frac {a}{2} \log (2a^2 - 2ax + x^2) + C$
• D. none of these

The average value of a function f(x) over the interval, [a,b] is the number $\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$
The square root $\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$ is called the root mean square of f on [a, b]. The average value of $\displaystyle \mu$ is attained id f is continuous on [a, b].