Find the area bounded by the curve $y=\left(4-x^2\right)$, the $y$-axis and the lines $y=0, y=3$.

Using integration, find the area of the region bounded by the triangle whose vertices are $A\left(-1,2\right), B\left(1,6\right)$ and $C\left(3,4\right)$.

Using integration, find the area of $△ABC$, the equation of whose sides $AB,BC$ and $AC$ are given by $y=4x+5, x+y=5$ and  $4y=x+5$ respectively.

Using integration, find the area of the region bounded between the line $x=2$ and the parabola $y^2=8x$.

Using integration, find the area of region bounded by the line $y-1=x$, the $x$-axis, and the ordinates $x=-2$ and $x=3$.

Sketch the region lying in the first quadrant and bounded by $y=4x^2, x=0, y=2$ and $y=4$. Find the area of the region using integration.

Sketch the region lying in the first quadrant and bounded by $y=9x^2, x=0, y=1$ and $y=4$. Find the area of the region, using integration.

Find the area of the region enclosed between the circles $x^2+y^2=1$ and ${\left(x-1\right)}^2+y^2=1$

Sketch the region common to the circle $x^2+y^2=16$ and the parabola $x^2=6y$. Also, find the area of the region, using integration.