Question

Find the total area between y=25-x2 and the x-axis for 0≤x≤7.5.


Round your answer to three decimal places.

The total area between y=25-x2 and the x-axis is what?

Answer 1

Step 1)

we know that total area under the curve y = f(x) and x -axis between x = a and x = b is given by,

where y = f(x) is above x axis between x = a and x = b

we know that total area under the curve y = f(x) and x -axis between x = a and x = b is given by,

where y = f(x) is below x axis between x = a and x = b

we can graph the curve y = 25 - x² between x = 0 and x = 7.5 as below :

Step 2)

we can see that between x = 0 and x = 5 curve y = 25 - x² is above x axis hence we can say that area under the curve y = 25 - x² and x axis between x = 0 and x = 5 is given by,

Step 3)

we can see that between x = 5 and x = 7.5 curve y = 25 - x² is below x axis hence we can say that area under the curve y = 25 - x² and x axis between x = 5 and x = 7.5 is given by,

Step 4)

we can say that total area is given by,

rounding to three decimal places we can say that,

Hence total area between y = 25 - x² and x - axis between x = 0 and x = 7.5 is 119.792