Mathematics

# Value of $I=\displaystyle \int_{0}^{\dfrac{\pi}{2}}\dfrac{(\sin x+\cos x)}{\sqrt{1+2x}}dx$ Then I=?

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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 Hard
$\displaystyle \int x\sin x\sec ^{3}x dx$ is equal to
• A. $\displaystyle \frac{1}{2}\left [ \sec^{2}x-\tan x \right ]+c$
• B. $\displaystyle \frac{1}{2}\left [ x\sec^{2}x+\tan x \right ]+c$
• C. $\displaystyle \frac{1}{2}\left [\sec^{2}x+\tan x \right ]+c$
• D. $\displaystyle \frac{1}{2}\left [ x\sec^{2}x-\tan x \right ]+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Find: $\int { \frac { cos\theta }{ (4+sin^{ 2 }\theta )(5-4{ cos }^{ 2 }\theta ) } d\theta }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Let $y = y(x), y(1)=1\ and\ y(e) ={e^2}$ . Consider
$J = \int {{{x + y} \over {xy}}} dy$, $I = \int {{{x + y} \over {{x^2}}}} dx$, $J - I = g\left( x \right)$ and g(1) = 1, then the value of g(e) is
• A. $e+1$
• B. ${e^2}$-e+1
• C. ${e^2}$+e-1
• D. $2e+1$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate:
$\int \dfrac{x+2^x.\log 2}{x^2+2^{x+1}}dx$

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].