Mathematics

The value of $\displaystyle \overset{\pi/2}{\underset{0}{\int}} \left(\sqrt{1 + 8 \sin^3 x} + (-2 \cos 2x + 4 \sin x + 2)^{\dfrac{1}{3}}\right)\cos x \,dx$ is equal to

$3$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

Q1 Subjective Hard
Solve:
$\int { \dfrac { dx }{ x({ x }^{ 7 }+1) } } =$ ?

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
lf $\displaystyle \int\frac{1}{1+\cot x}dx=_{A}$ Iog $|Sinx+$ Cos $x|+$ Bx $+c$, then $A=\ldots\ldots..,\ B=\ldots\ldots\ldots.$,
• A. $-1, 1$
• B. $\displaystyle \frac{1}{3},\frac{1}{2}$
• C. $\displaystyle \frac{-1}{3},\frac{1}{2}$
• D. $-\displaystyle \frac{1}{2},\frac{1}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $g(x)$ is a differentiable function satisfying $\dfrac{d}{dx}{g(x)}=g(x)$ and $g(0)=1,$ then $\int { g\left( x \right) } \left( \dfrac { 2-sin2x }{ 1-cos2x } \right) dx$ is equal to
• A. $-g(x)cot$ $x+C$
• B. $\dfrac{g(x)}{1-cos2x}+C$
• C. $None$ $of$ $these$
• D. $g(x)cot$ $x+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to
• A. $2\ \sin\ x-\ell\ n|\sec\ x-\tan\ x|\ + C$
• B. $2\ \sin\ x+\ell\ n|\sec\ x+\tan\ x|\ + C$
• C. $\ \sin\ x-\ell\ n|\sec\ x+\tan\ x|\ + C$
• D. $2\ \sin\ x-\ell\ n|\sec\ x+\tan\ x|\ + C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
Let $\displaystyle I_1 = \int_1^2 \frac{1}{\sqrt{1 + x^2}} dx$ and $I_2 \displaystyle = \int_1^2 \frac{1}{x} dx$. Then
• A. $I_1 > I_2$
• B. $I_1 = I_2$
• C. $I_1 > 2 I_2$
• D. $I_2 > I_1$