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Determine the area under the curve

y = 4 - x^2

from

x = -2

x = 2

Apr 30, 2024

Determine the area under the curve

y = 4 - x^2

from

x = -2

x = 2

Generated Graph

Solution by Steps

step 1

Calculate the definite integral of the function

4 - x^2

from

-2

2

step 2

The antiderivative of

4 - x^2

4x - \frac{x^3}{3}

step 3

Evaluate the antiderivative at the upper limit of integration:

4(2) - \frac{2^3}{3} = 8 - \frac{8}{3} = \frac{24}{3} - \frac{8}{3} = \frac{16}{3}

step 4

Evaluate the antiderivative at the lower limit of integration:

4(-2) - \frac{(-2)^3}{3} = -8 - \frac{-8}{3} = -8 + \frac{8}{3} = -\frac{24}{3} + \frac{8}{3} = -\frac{16}{3}

step 5

Subtract the value of the antiderivative at the lower limit from the value at the upper limit:

\frac{16}{3} - (-\frac{16}{3}) = \frac{16}{3} + \frac{16}{3} = \frac{32}{3}

Answer

\frac{32}{3}

or approximately

10.667

Key Concept

Definite Integration

Explanation

The area under the curve

y = 4 - x^2

from

x = -2

x = 2

is found by evaluating the definite integral of the function over the given interval.