Area Under The Curves - Calculus - Mathematics Previous Year Questions

Circle centered at origin and having radius \(\pi\) units is divided by the curve y = sin x in two parts. Then area of upper parts equals to

The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

The area enclosed by the curves \(y = \sin x + \cos x\) and \(y = |\cos x - \sin x|\) over the interval \(\left[ {0,{\pi \over 2}} \right]\) is

What is the area enclosed by the parabola described by \({(y - 2)^2} = (x - 1)\), its tangent line at the point (2, 3), and the X-axis?

The area of the region bounded by the parabola \(y=x^2+1\) and lines \(y=x+1, y=0, x=\frac{1}{2}\) and \(x=2\) is

Let the functions \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=e^{x-1}-e^{-|x-1|}\) and \(g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)\). Then, the area of the region in the first quadrant bounded by the curves \(y=f(x), y=g(x)$ and $x=0\) is.

What is the area enclosed by the curves $y=x^4$ and $y=x^{\frac{1}{3}}$