Find the area under the curve y=sqrt(4-x^2) that lies between x=1and x=2.
Can someone tell me the steps needed to solve problems like this

Question

Find the area under the curve y=sqrt(4-x^2) that lies between x=1and x=2. 
Can someone tell me the steps needed to solve problems like this

zepdrix · Answer

Ahhhh I'm so tired >.< I dunno if I have the energy for another math problemmmmm.

Ok ok ok, let's try

anonymous · Answer

lol ok thank you

zepdrix · Answer

It really helps if you're able to graph this,
if not, it'll still work out ok.

Do you understand what shape we get from that square root function?

anonymous · Answer

is the shape going to be half a circle?

zepdrix · Answer

Top half of a circle? Ok good, y a :)

anonymous · Answer

can i solve it without graphing though...

zepdrix · Answer

Ah, yes fine. Be that way. :3

zepdrix · Answer

Since our function lies above the x-axis, it's simply:$$\Large\rm \int\limits \sqrt{4-x^2}dx$$And ya, we can throw the boundaries in there :)

zepdrix · Answer

Do you need help dealing with this integral?
Feels like a nice spot for a Trig Sub.

anonymous · Answer

would the boundaries be 1 and 2?

zepdrix · Answer

Mmmm ya that seems about right,$$\Large\rm \int\limits\limits_1^2 \sqrt{4-x^2}dx$$

zepdrix · Answer

|dw:1430712881214:dw|This is kind of what it would look like ya?