Question

find the net area and the area of the region above the x - axis bounded by ( y = 49 - x^{2} ). graph the function and indicate the region in question. the integral needed to compute the net area is (type an exact answer.)

Explanation:

Step1: Find x-intercepts

To find where \( y = 49 - x^2 \) intersects the x - axis, set \( y = 0 \):
\( 0=49 - x^2 \)
\( x^2 = 49 \)
\( x=\pm7 \)

Step2: Set up the integral for net area

The net area between a function \( y = f(x) \) and the x - axis from \( x = a \) to \( x = b \) is given by the definite integral \( \int_{a}^{b}f(x)dx \). Here, \( f(x)=49 - x^2 \), \( a=- 7 \) and \( b = 7 \). So the integral for the net area is \( \int_{-7}^{7}(49 - x^2)dx \)

Answer:

\(\int_{-7}^{7}(49 - x^2)dx\)