Mathematics

# Evaluate $\displaystyle \int \dfrac{dx}{\left ( 16x^{2}-25 \right )}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int _0^{\pi /2} f(\sin 2x)\sin x\, dx = K\int_0^{\pi/2} f(\cos 2x) \cos x\,dx$ where $k$ equals to
• A. $4$
• B. $\sqrt{2}$
• C. $2\sqrt{2}$
• D. $2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int \dfrac{1}{3\sin x +4\cos x} dx$ equal, where $\tan \alpha = \dfrac{4}{3}$
• A. $\dfrac{1}{5} ln \left|\tan \left(x+\alpha\right)\right|+K$
• B. $\dfrac{1}{5} ln \left|\tan \left(\dfrac{x}{2} +\dfrac{\pi}{2}- \dfrac{\alpha}{2}\right)\right|+K$
• C. $\dfrac{1}{5} ln \left|\tan \left(\dfrac{x}{2} -\dfrac{\alpha}{2}\right)\right|+K$
• D. $\dfrac{1}{5} ln \left|\tan \left(\dfrac{x}{2} + \dfrac{\alpha}{2}\right)\right|+K$

1 Verified Answer | Published on 17th 09, 2020

Q3 One Word Medium
$\int \dfrac{1}{x\sqrt{1+\ln x}} dx=m\sqrt{(1+\ln x)}+c$.Find $m$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle \frac{(x^2+1)}{(x^2+2)(x^2+3)}=\frac{-1}{x^2+2}+\frac{\alpha}{x^2+3}$, then $\alpha =$
• A. $1$
• B. $3$
• C. $4$
• D. $2$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
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].