Calculate the total area of the region bounded by the curve y = sqrt(x), the x-axis, and the lines x=0 and x=25.
To find the required area we need to calculate the definite integral of the function y = sqrt x, between the limits x = 0 and x = 25.
First let us find the indefinite integral of y = sqrt x
y = sqrt x = x^(1/2)
Now the integral of x^n = x^(n+1)/ (n+1)
Int[y] = x^(3/2) / (3/2)
=> (2/3)* x^(3/2) + C
For x = 0, this is equal to
0 + C = C
For x = 25, this is equal to
(2/3)*25^(3/2) + C
=> (2/3)*125 + C
The difference of the two is equal to:
(2/3)*125 + C - C
=> 250 / 3.
Therefore the required area is 250/3.