Question

Sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r > 0)

Answer 1

Step 1:

The area of the function is .

Graph the function .

Observe the graph:

The graph of the function is the upper part of the circle with radius 7.

The region under the semicircle is the area of the function which is shaded in the interval .

Step 2:

The area of the function is  .

Solution: