Question

What is a strategy to evaluate INT(sqrt(a-x^2)dx) ?

Answer 1

put x= a sin(t)

Answer 2

i'm the least experienced with trig substitution, can you show me the next step? my problem is that i keep ending up with two terms under the sqrt and they don't make another trig identity.

Answer 3

x= a sin(t)
dx/dt= a cost

Answer 4

dx= a cost dt

Answer 5

i imagine what i'm trying to get is a trig function squared under the square root so that they cancel, is there another way that would get rid of that square root?

Answer 6

here is what u get

Answer 7

hey in ur question is it a or a^2?

Answer 8

a

Answer 9

ok...do integration by parts..u know how to do that.......I've done it on paper ..it works

Answer 10

so x=sin (t), and int by parts as well?

Answer 11

no just integration by parts without any substitution

Answer 12

so u=a-x^2 and dv=sqrt(u)du ?

Answer 13

dont substitute, take the whole square root thing as first term and 1 as second term. okay?

Answer 14

i don't get it, it just seems to prolong the problem. i still have two terms under the sqrt.