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.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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