The term integration refers to the areas of the two-dimensional regions, including calculating the 3-D volumes of objects. When we find the integral function of x, we get it along with the X-axis area. A problem related to the application of integrals is as follows:
Given parabola condition is y2 = 8x.
Condition of line is x = 2.
Here, y2 = 8x as a right given parabola having its vertex at the beginning, and x = 2 is the line corresponding to y-pivot at x = 2 units distance.
Additionally,
y2 = 8x has just even force of y and is balanced about x-hub.
Along these lines, the necessary region = Area of OAC + Area of OAB.
= 2 (Area of OAB)
= 2 ∫02 y dx
Subbing the worth of y, for example y2 = 8x and y = √(8x) = 2 √2 √x, we get;
= 2 ∫02 (2 √2 √x) dx
= 4√2 ∫02 (√x) dx
= 4√2 [x3/2/(3/2)]02
By applying the cutoff points,
= 4√2 {[23/2/(3/2)] - 0}
= (8√2/3) × 2√2
= (16 × √2 × √2)
= 32/3
Go through the model given underneath to figure out how to track down the area between two bends.