Question

Evaluate by interpreting it in terms of areas.

Answer 1

\[\int\limits_{0}^{1}x + \sqrt{1-x^2}dx\]

Answer 2

Any ideas??

Answer 3

Its given an area under curve y = x+root(1−x2)

Answer 4

more precisely, area under curve, line x=1, x=0 and y=0

Answer 5

Ok

Answer 6

Sooo what do i do?? Im still confused

Answer 7

you integrate first than find the value of inegration when x=0 and when x=1....subtract answer from x=1 to x=0..so thats the area

Answer 8

The first term represents the area of a triangle with base and height equal to 1 unit length. Its area is equal to 1/2(1)(1)=1/2.

Answer 9

The second term represents the part in the first quadrant of a circle centered at the origin and with radius one. Its area is 1/4*pi*1=pi/4. So the value of the given integration is 1/2+pi/4=(2+pi)/4.

Answer 10

^^ You are a life saver!! Thank you sooo much!!

Answer 11

Glad to help!