Find the area between the graph of y = x^2 - 2 and the x-axis, between x = 0 and x = 7.?

Question

I can not for the life of me figure out the answer to this question. I keep getting 100.333 but it says that's not correct. any help will be greatly appreciated! thanks!

Answer 1

First find the area bounded by y=x^2-2 and x-axis.

First, find the x-intercepts  when y = 0 to find the limits of integration:

y = x² - 2

x² - 2=0

x² = 2

x = ±√ 2

The x-intercepts are x = +√ 2 and -√ 2.

Therefore the limits of integration are +√ 2 and -√ 2.

Area is

Now find the area when x=0 and x=7:

The area between the graph of y=x^2 - 2 and the x-axis, between x=0 and x=7 is area bounded between x=0 and x=7 minus area bounded by y=x^2-2 and x-axis.

The answer is 104.104 squareunits.