Application of ...

The area enclosed between the curves $$y=log_e(x+e), x=log_e\left(\dfrac{1}{y}\right)$$ and the x-axis is?

The area (in sq. units) bounded by the parabola $$y=x^{2}-1$$ , the tangent at the point (2,3) to it and the y-axis is:

The area bounded by the curve $$y \le x^2 + 3x , 0 \le y \le 4, \, 0 \le x \le 3$$ , is

The area bounded by the curve $$y=x$$ $$X-$$axis and the lines $$x=-1$$ and $$x=1$$ is

The area of the region bounded by the curve $$y=\phi(x),y=0$$ and $$x=10$$ is

If the area (in sq. units) of the region $$\{(x, y): y^2\le 4x, x+y\le 1, x\geq 0, y\ge 0 \}$$ is $$a\sqrt{2}+b$$, then $$a-b$$ is equal to?

Let $$f(x, y)=\{(x, y): y^2 \leq 4x, 0\leq x\leq \lambda\}$$ and $$s(\lambda)$$ is area such that $$\dfrac{S(\lambda)}{S(4)}=\dfrac{2}{5}$$. Find the value of $$\lambda$$.

Region formed by $$|x-y| \le 2$$ and $$|x + y| \le 2$$ is

The region represented by $$|x - y| \le 2$$ and $$|x + y| \le 2$$ is bounded by a:

The area (in sq. units) of the region $$A=\{(x, y):x^2\leq y\leq x+2\}$$ is?