- #1
rhyso88
- 8
- 0
Hi, i am hoping that someone could help me or give me a hint for the follwing question...i will show what I have done so far
The area of a quarter circle given is
Integral sqrt(25-x^2) dx
Use the substitution x = 5 sinu to evaluate this def integral exactly an show that your answer is consistent with area pi*r^2 with radius r
firstly i did dx/du = 5cos u
then i said:
Integral 5sqrt(1-sin^2u).5cosu du
Integral 5cosu.5cosu
Integral 25 cos^2u du
Integral 25(1+cos2u)/2
Integral 25/2 +25cos2u/2
and well the problem i am having is that i don't know how to get the u =5sin u to SUB into the intergal so i can solve it (ie i can SUB u into cos2u...it doesnlt work)
so hopefully someone could point me in a better diretion to solve this??
thanks heaps!
The area of a quarter circle given is
Integral sqrt(25-x^2) dx
Use the substitution x = 5 sinu to evaluate this def integral exactly an show that your answer is consistent with area pi*r^2 with radius r
firstly i did dx/du = 5cos u
then i said:
Integral 5sqrt(1-sin^2u).5cosu du
Integral 5cosu.5cosu
Integral 25 cos^2u du
Integral 25(1+cos2u)/2
Integral 25/2 +25cos2u/2
and well the problem i am having is that i don't know how to get the u =5sin u to SUB into the intergal so i can solve it (ie i can SUB u into cos2u...it doesnlt work)
so hopefully someone could point me in a better diretion to solve this??
thanks heaps!