Question

Help Trigonometric substitution
\[\int\limits_{5}^{10}\sqrt{100-x ^{2}}dx\]

Answer 1

same hint :
a^2-x^2
put x= a sin theta

Answer 2

let x = 10sin(x)

Answer 3

\[\sqrt{100-(10\sin \theta)^{2}}dx\]

Answer 4

\[\sqrt{100-100\sin ^{2}x}\]

Answer 5

Then use a trig identity

Answer 6

then dx= 10 cos t

Answer 7

Yes, let me work out the full problem real quick

Answer 8

yes, ans what does sqrt (....) simplify to ?

Answer 9

so will it eventually just be 100 cos^2 t

Answer 10

yes.
and you know the cos 2x formula ?

Answer 11

cos^2 t = (1+cos2 t)/2
that one?

Answer 12

yes

Answer 13

yes, that should make it easier to solve now :)

Answer 14

alright thanks so much again

Answer 15

ask if you get stuck again anywhere....