Figure shows the curve y=x2.Find the area of the shaded part between x=0 and x=6
72 unit2
The area can be divided into strips by drawing ordinates between x = 0 and x = 6 at a regular interval of dx. Consider the strip between the ordinates at x and x + dx. The height of this strip is y=x2. The area of this strip is dA = y dx = x2dx.
The total area of the shaded part is obtained by summing up these strip-areas with x varying from 0 to 6. Thus
A=6∫0x2 dx
=[x33]60=216−03=72