微積分作業(急) 請大大幫忙?

(1) ∫(x=0~2)∫[y=x~√(8-x^2)]√(x^2+y^2)*dy*dx

= ∫(Q=0~π/4)∫(r=0~2√2) r*(r*dr*dQ)

= (c)


Note:

x = 2√2*cosQ = 2

=> cosQ = 1/√2

=> Q = π/4




(2) ∫(x=0~9)∫(y=0~√x)f(x,y)dydx

= ∫(y=0~3)∫(x=0~y^2)f(x,y)dx*dy

= (a)


Note: x = y^2

=> y^2 = x = 9

=> y = 3



(3) y = 4 - x ==> x = 4 - y

∫∫f(x,y)dA

= ∫(y=a~b)∫[x=h1(x)~h2(x)]f(x,y)dx*dy

=> h1(x) = 0 = (e)




(4) ∫∫f(x,y)dA

= ∫(x=a~b)∫[y=g1(x)~g2(x)]f(x,y)dy*dx

=> g1(x) = 0 = (b)



(5) y = 4 - x ==> x = 4 - y

∫∫f(x,y)dA

= ∫(y=a~b)∫[x=h1(x)~h2(x)]f(x,y)dx*dy

=> h2(x) = 4-y = (b)

.........