Question

graph the integrand

Answer 1

http://www.wolframalpha.com/

Answer 2

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

Answer 3

lmfao really..

Answer 4

graph the integrand, and use known area formulas, to determine the area.

Answer 5

im not sure what formula i should use.

Answer 6

Are you allowed a graphing Calc?

Answer 7

no.

Answer 8

Integrating is actually taking the area under the curve, so in theory you've just got to find the values of the integrand between x=-1 and x=1 Don't forget that to switch the boundaries around you have to switch the sign.

Answer 9

yeah... but i have to use known area formulas, i can't just find the integral and then sub in x=-1 and x=1

Answer 10

In this case you would use, trig substitution. Find your antiderivative and evaluate

Answer 11

y=1+sqrt(1-x^2)
y-1=sqrt(1-x^2)
(y-1)^2=1-x^2
x^2+(y-1)^2=1
Graph the top part of the circle.

Answer 12

Its seems to me that it would be the circle. Due to the consistent radius throughout the circle.

Answer 13

Would the answer just be pi/2 then? since the radius is 1, and the formula for the area of half a circle is pi multiplied by r^2 all over 2

Answer 14

or would i have to calculate the area from the half circle to x-axis?

Answer 15

well you have a half because it says from -1 to 1
if it was a quarter it would be 0 to 1 ( or -1 to 0)