# How do you use integrals to find the area bounded by the curve y = (x^2 - 9) and the x-axis for x = 0 to x = 5?

I found: area

You write it as:

you can break it into two as:

integrating you get:

now you use you extremes of integration substituting them and subtracting the resulting expressions as:

You may wonder about the negative sign but looking at your area:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area bounded by the curve ( y = x^2 - 9 ) and the x-axis for ( x = 0 ) to ( x = 5 ), you integrate the absolute value of the function ( y = x^2 - 9 ) with respect to ( x ) from ( x = 0 ) to ( x = 5 ). The integral is:

[ \int_{0}^{5} |x^2 - 9| , dx ]

Split the integral at the points where ( x^2 - 9 = 0 ), which are ( x = -3 ) and ( x = 3 ). Then integrate each portion separately and take the absolute value since the function changes sign between ( x = -3 ) and ( x = 3 ). Calculate the integral for each portion and sum them to find the total area.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you evaluate the definite integral #int sqrtx(1-x)dx# from [0,1]?
- What is the antiderivative of #m(x) = (-2/y^3)#?
- What is the antiderivative of #1/cosx(2+sinx)#?
- How do you evaluate the integral #int x dx# from #-oo# to #oo# if it converges?
- How do you find the antiderivative of #f(x) = 1 / (5cos^2(5x))#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7