### Application of Integrals

goals
Let $O\left( {0,0} \right)\,A\left( {2,0} \right)\,and\,B\left( {1,\frac{1}{{\sqrt 3 }}} \right)$ be the vertices of a triangle. Let $R$ be the region consisting of all those points $p$ inside $\Delta QAB$ which satisfy $d,(P,OA) \le$ min $\left\{ {d(\left( {P,OB} \right),d\left( {P,AB} \right)\left. ) \right\}} \right.$ when $'d'$ denotes the distance from the point to the corresponding line. Then the area of the region $R$ is $\sqrt a - \sqrt {b}$ then $a+b=$
Area common to the curves ${ y }^{ 2 }$=ax and ${ x }^{ 2 }$+${ y }^{ 2 }$$= 4ax$ is equal to
The area bounded by the curve $y=\cos\,x$, the line joining $\left(-\dfrac{\pi}{4},\cos\left(-\dfrac{\pi}{4}\right)\right)$ and $(0,2)$ and the line Joining $\left(\dfrac{\pi}{4},\cos\left(\dfrac{\pi}{4}\right)\right)$ and $(0,2)$ is
The areas ${S}_{1},{S}_{2},{S}_{3}$ bounded by $x-$axis and half waves of the curves $y={e}^{-ax}\sin{\beta x},x\ge 0$ from left to right then:
What is the area bounded by the curve ${y}^{2}=4x$ and the double ordinate $x=1$?