Mathematics

# $\int { \dfrac { \cos { x } }{ { \left[ \cos { \left( \dfrac { x }{ 2 } \right) } +\sin { \left( \dfrac { x }{ 2 } \right) } \right] }^{ 5 } } dx= }$

$\dfrac { 2 }{ 3 } { \left[ \csc { \left( \dfrac { x }{ 2 } \right) +\sec { \left( \dfrac { x }{ 2 } \right) } } \right] }^{ 3 }+C$

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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
A tank initially holds 10 lit. of fresh water. At t = 0, a brine solution containing $\displaystyle \frac{1}{2}$ kg of salt per lit. is poured into tank at a rate 1 lit/min while the well-stirred mixture leaves the tank at the same rate. Find the amount of salt in a tank at a particular time
• A. $5e^{-t} + 5$
• B. $5e^{-t} - 5$
• C. $-5e^{} - 5$
• D. $- 5e^{-t} + 5$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle\int^{\pi/2}_0\sin^2xdx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium

Evaluate the following definite integral:

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

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Integrate the following function
$x\ \sin^{-1}x$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$