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 of the region bounded by the parabola $$y=x^2$$ and the curve $$y=|x|$$ is

The area bounded by the $$\mathrm{X}$$-axis and the curve $$y=x(x-2)(x+1)$$ is

Area of the region bounded by the curve $$y=\sqrt{49-x^2}$$ and $$\mathrm{X}$$-axis is

If $$\mathrm{f}^{\prime}(x)=x-\frac{5}{x^5}$$ and $$\mathrm{f}(1)=4$$, then $$\mathrm{f}(x)$$ is

The area (in sq. units) bounded by the curve $$y=x|x|, \mathrm{X}$$-axis and the lines $$x=-1$$ and $$x=1$$ is

The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is

The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is

The area of the region bounded by the curve y$$^2$$ = 4x and the line y = x is

The area bounded by the parabola $$y=x^2$$ and the line $$y=x$$ is

The area of the region bounded by the parabola x$$^2$$ = y and the line y = x is