Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. -5∫ 5 sqrt( 5^ 2 − x^ 2) d x

Question

Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry.-5

my lower limit is -5 and my upper is 5. How do I solve this problem? do i graph this equation and use left or right approximation?

Answer 1

Bri

The integral represents the area between y = √ (25 - x²) and the x axis for -5<=x<=+5

The equation of a circle centre (0,0) radius 5, is x² + y ² = 25, and if you rearrange this you will get the above expression for y.

In other words if you draw this curve you will get a semi circle. (you only take the positive square root so y>=0).

So you have to find the area of the semicircle ... hopefully you know how to do that !

Mike