Question

Sketch the region lying in the first quadrant and bounded by y = 9x², x = 0, y = 1 and y = 4. Find the area of the region, using integration.

Answer 1

Here x² = 1/9 y is a upward parabola having its vertex at the origin and y = 1, y = 4 are the lines which are parallel to x-axis at y = 1 to y = 4 units distance from it.

Similarly x² = 1/9 y has even power of y and is symmetrical about y-axis

So the required area is written as