Question

evaluate s x( (8+2x-x^2) )^1/2 dx

p/s: s is for integrate

Answer 1

I assume its an integral
\[\int\limits x\sqrt{8+2x-x^{2}}dx \]
Well, complete the square first; then looks like a sub

Answer 2

yes. I've done the completing the square but not sure whats the next step. by part or substitution?

Answer 3

looks like a substitution would be easier

Answer 4

ok. i"ll try again. tq :)

Answer 5

still dont get it. help me plez :(

Answer 6

\[\int\limits x\sqrt{-x^{2}+2x+8} dx => \int\limits x\sqrt{-(x^{2}-2x-8)} dx => \int\limits x\sqrt{-((x^{2}-1)^{2}-(1)^{2}+8))} dx\]
\[=> \int\limits x\sqrt{-(x^{2}-1)-9} dx => \int\limits x\sqrt{9-(x-1)^{2}} dx\]
let u = x-1 -> x = u+1
\[=> \int\limits\left(u+1\right)\sqrt{9-u^{2}}du \]

Answer 7

then it's trig sub

Answer 8

\[ x= sin\theta\]

Answer 9

ok mimi.i'll try. thanks again.

Answer 10

np
and for this u = 3sin\theta