Question Text
Question 1 :
If $f(x)=\begin{cases}x^{2} & \text{ for } 0\leq x\leq 1 \\ \sqrt{x} & \text{ for } 1\leq x\leq 2 \end{cases}$ then $\displaystyle \int_{0}^{2}f(x)dx=$<span><br></span>
Question 4 :
Evaluate the following integral by expressing them as a limit of a sum.<br/>$\int^{2}_1(3x-2)dx$
Question 7 :
$\displaystyle \mathop {\lim }\limits_{x \to 0} \dfrac{{ \displaystyle \int\limits_0^x {{{\left( {{t^2} + {e^{{t^2}}}} \right)}^{\tfrac{1}{{1 - \cos t}}}}} } } {{\left( {{e^x} - 1} \right)}} dt $ is equal to:
Question 8 :
The value of the integral $\displaystyle \int_0^1 \dfrac{x^3}{1 + x^3} dx$ is equal to
Question 10 :
The value of the integral $\displaystyle\int^1_0\dfrac{dx}{x^2+2x\cos \alpha +1}$, where $0 < \alpha < \dfrac{\pi}{2}$, is equal to
Question 12 :
<span>Consider the integral $I=\displaystyle\int^{\pi}_0 ln(\sin x)dx$.</span>What is $\displaystyle\int^{\dfrac{\pi}{2}}_{0}$ ln $(\sin x)dx$ equal to?
Question 15 :
$\displaystyle \underset{0}{\overset{\pi}{\int}} \dfrac{x \, dx}{1 + \sin \, x} = $
