Could someone please explain to me what it means when I have to give a geometric interpretation of each term of the integral, say, between x = b and x = 0?
From what I can make of the question, all I can think of is that a is the radius of the semicircle.
Please help?
the inetgral gives the area under the semi-circle and above the x-axis between x = 0 and x = b
it does not seem that way
actually, no. if you differentiate that, you do not get the original integrand...
why do you not follow the hint? (write it as x = asin(u) though...)
Well using the standard trigonometric substitution method...and going back to our original integral i got..
from x = 0 to x = b...
so use the substitution and
so the integral becomes
which becomes
so we finally get
We have to also change our limits of integration... from x = 0 to = 0 and we get that x = b turns to =
so my final answer was...