Question

Find the area between the curve and the​ x-axis over the indicated interval.

y = 100 − x²​;

  

​[−10​,10​]

The area under the curve is ___

​(Simplify your​ answer.)

Answer 1

we know that area between the curve y = f(x) and x axis over the interval [a,b] is given by,

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

we can graph the curve y = 100 - x² between x = -10 and x = 10 as below:

we can see that y = 100 - x² is above x axis between x = -10 and x = 10 hence area is given by,

we can also write,

rounding to 4 decimal places

Hence we can say that,

or,