∬Rsin(x2+y2)dA,R={16≤x2+y2≤25}
x=rcosϕy=rsinϕI=r
Find the integration limits:
ϕ∈[0,2π]
16≤x2+y2≤2516≤r2cos2ϕ+r2sin2ϕ≤2516≤r2≤254≤r≤5
r∈[4,5]
So:
∬Rsin(x2+y2)dA=∫45dr∫02πrsin(r2)dϕ==∫45rsin(r2)drϕ∣02π=2π∫45rsin(r2)dr==[r2=u2rdr=du5→254→16]=π∫1625sin(u)du==−πcos(u)∣1625=π(cos16−cos25)==2πsin(241)sin(29)
Comments
Thank you for correcting us.
Hello, you made a big mistake here. The integrated was sin(x^2+y^2) not x^2+y^2
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