Question Text
Question 1 :
$\displaystyle \int (1 + x - x^{-1})e^{x + x^{-1}}dx$ is equal to
Question 4 :
What is $\int \dfrac {xe^{x}dx}{(x + 1)^{2}}$ equal to?<br>where $c$ is the constant of integration.
Question 5 :
The solution for $x$ of the equation $\int_{\sqrt{2}}^{x} \dfrac{d t}{t \sqrt{t^{2}-1}}=\dfrac{\pi}{2}$ is
Question 11 :
Value of $\int_{\pi}^{2 \pi} [2 \, sin \, x] dx $where [ ] represents the greatest integer function is
Question 13 :
$\displaystyle \int _{ 0 }^{ { \pi }/{ 8 } }{ { \cos }^{ 3 } } 4\theta d\theta $ is equal to:
Question 15 :
If $ I_n = \int_0^{\pi /4}\tan^n dx , $ then $ \dfrac {1}{I_2 + I_4} \dfrac {1}{I_3 + I_5} \dfrac {1}{I_4 + I_6} $ is :
Question 16 :
<p>Consider the integrals ${I_1} = \int_0^1 {{e^{ - x}}{{\cos }^2}xdx,} {I_2} = \int_0^1 {{e^{ - {x^2}}}{{\cos }^2}xdx,} {I_3} = \int_0^1 {{e^{ - x}}dx} $ and ${I_4} = \int_0^1 {{e^{ - (1/2){x^2}}}} dx$. The greatest of these integrals is</p><p></p>
Question 18 :
The solution of $\displaystyle \int_{\sqrt {2}}^{x} \dfrac {dt}{\sqrt {t^{2} - 1}} = \dfrac {\pi}{12}$ is
Question 19 :
The values of $x$ for the given equation ${\sec ^{ - 1}}\left( x \right) - {\sec ^{ - 1}}\left( {\sqrt 2 } \right) = \frac{\pi }{2}$ is
Question 20 :
What is $\displaystyle \int _{ 0 }^{ \pi }{ { e }^{ x } } \sin { x } dx$ equal to?