Question

Find the area bounded by the graphs of the indicated equations over the given interval.
y=x²-25; y = 0; -3≤x≤0

Answer 1

Answer:

48

Step-by-step explanation:

$y = 0$

is basically the horizontal axis.

First, find the integral of x^2-25.

Remember that

integral of a constant is that constant times x.

Also that

to take the integral of a power function, add 1 to the degree and divide by that same degree.

$y = {x}^{2} - 25$

We then get

$\frac{ {x}^{3} }{3} - 25x$

Evaluate at -3

$\frac{ - 3 {}^{3} }{3} - 25( - 3)$

$- 27 + 75 = 48$

Then we evaluate at 0

$\frac{0 {}^{3} }{3} - 25(0) = 0$

Next, we subtract the the answer then we get

$48 - 0 = 48$