Question Text
Question 1 :
The area bounded by the curves $y = \log _ { e } x$ and $y = \left( \log _ { e } x \right) ^ { 2 }$ is
Question 2 :
If the area above x-axis bounded by the curves $y = 2^{kx}, x = 0$ and $x = 2$ is $\dfrac{3}{\log \, 2}$, then the value of $k$ is
Question 3 :
Area bounded by the curve $y= sin^{-1}x, y-axis$ and $y = cos^{-1}x$ is equal to
Question 4 :
$Letf(x)={ sin }^{ -1 }(sin\quad x)+{ cos }^{ -1 }(\quad cos\quad x),\quad g(x)=mx\quad and\quad h(x)=x\quad $ are three functions. Now g(x) is divided area between f(x),x=$\pi $ and y=0 into two equal parts.<br/>The area bounded by the curve y=f(x), x=$\pi $ and y=0 is:
Question 5 :
The area bounded by $\displaystyle y={ xe }^{ |X| }$ and$\displaystyle |x|=1$ is -
Question 6 :
Area bounded by the line $y=x,$ curve $y=f\left(x\right),\left(f\left(x\right)>x,x>1\right)$ and the lines $x=1,x=t$ is $\left(t+\sqrt{\left(1+{t}^{2}\right)}\right)-\left(1+\sqrt{2}\right)$ for all $t>1$. Then $f\left(x\right)=$
Question 7 :
The area common to the circle ${x}^{2}+{y}^{2}=16{a}^{2}$ and the parabola ${y}^{2}=6ax$ is
Question 8 :
The value of $'a'$ for which the area of the triangle included between the axes and any tangent to the curve ${x}^{a}y={\lambda}^{a}$ is constant, is/are
Question 10 :
The area inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$, is