find the area bounded by the graphs of the indicated equations over the given interval. y = x^2 - 5; y = 4…

find the area bounded by the graphs of the indicated equations over the given interval. y = x^2 - 5; y = 4; 0 ≤ x ≤ 3\nthe area is square units. (type an integer or decimal rounded to three decimal places as needed.)

find the area bounded by the graphs of the indicated equations over the given interval. y = x^2 - 5; y = 4; 0 ≤ x ≤ 3\nthe area is square units. (type an integer or decimal rounded to three decimal places as needed.)

Answer

Explanation:

Step1: Identify upper and lower functions

Upper: ( y=4 ), Lower: ( y=x^2-5 )

Step2: Set up integral

Area = ( \int_{0}^{3} [4 - (x^2 - 5)] dx = \int_{0}^{3} (9 - x^2) dx )

Step3: Compute antiderivative

Antiderivative: ( 9x - \frac{x^3}{3} )

Step4: Evaluate from 0 to 3

At 3: ( 9*3 - \frac{3^3}{3} = 27 - 9 = 18 ); At 0: 0

Step5: Calculate area

Area = 18 - 0 = 18

Answer:

18