The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is

The area (in sq. units) of the smaller part of the circle $$x^2+y^2=\mathrm{a}^2$$ cut off by the line $$x=\frac{\mathrm{a}}{\sqrt{2}}$$ is

The area of the region bounded by the curves $$y=\mathrm{e}^x, y=\log x$$ and lines $$x=1, x=2$$ is

The slope of the tangent to a curve $$y=\mathrm{f}(x)$$ at $$(x, \mathrm{f}(x))$$ is $$2 x+1$$. If the curve passes through the point $$(1,2)$$, then the area (in sq. units), bounded by the curve, the $$\mathrm{X}$$-axis and the line $$x=1$$, is