Application of ...

The line $$2y=3x+12$$ cuts the parabola $$4y=3x^2$$. What is the area enclosed by the parabola and the line?

The area in the first quadrant between $$x^2 + y^2 = \pi^2$$ and $$y = sin  x$$ is

Consider the curves $$y = \sin x$$ and $$y = \cos x$$.

The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x = 0$$ and $$x = \dfrac {3\pi}{2}$$ is

Consider the curves $$y = \sin x$$ and $$y = \cos x$$.

The area of the region bounded by the lines $$y = 2x + 1, y = 3x + 1$$ and $$x = 4$$ is

The area bounded by the curves $$y=\cos x$$ and $$y=\sin x$$ between the ordinates $$x=0$$ and $$x=\displaystyle\frac{3\pi}{2}$$ is?

The line $$x=\dfrac{\pi}{4}$$ divide the area of the region bounded by $$y=\sin x, y = \cos x$$ and X-axis $$\left(0 \le x \le \frac{\pi}{2}\right)$$ into two regions of areas $$A_1$$ and $$A_2$$. Then, $$A_1:A_2$$ equals

The area bounded by the parabola $${ y }^{ 2 }=4a(x+a)$$ and $${ y }^{ 2 }=-4a(x-a)$$ is

Consider an ellipse $$\cfrac{x^2}{a^2}+\cfrac{y^2}{b^2}=1$$ What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?