Question

g Determine the area of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

Answer 1

Answer:

A = 166.66

Step-by-step explanation:

You have the following functions:

$y_1=x^2-24\\\\y_2=1$

In order to calculate the area of the given region, you first calculate the points at which the function y = x^2-24 intersects the line y=1:

$1=x^2-24\\\\0=x^2-25\\\\x=\sqrt{25}=\pm 5$

Next, you take into account that the area between the two function is given by:

Where you have used the fact that y2 is above the y1 function.

Next, you calculate the following integral:

$A=\int_{-5}^{5}(1-(x^2-24))dx=\int_{-5}^{5}(25-x^2)dx\\\\A=(25x-\frac{1}{3}x^3)|_{-5}^{5}\\\\A=(25(5)-\frac{1}{3}(125))-(25(-5)-\frac{1}{3}(-125))\\\\A=166.66$

Then, the area of the bounded region is 166.66