In the following exercises, the function f is given in terms of double integrals. a. Determine the explicit form of the function f. b. Find the volume of the solid tinder the surface z = f(x. v) and above the region R. C. Find the average value of the function f on R. d. Use a computer algebra system (CAS) to plot z = f(x. y) and z = f a v e in the same system of coordinates. 51. Show that if f and g are continuous on [ a , b ] and [ c , d ], respectively, then ∫ c b ∫ a d [ f ( x ) + g ( y ) ] d y d x = ( d − c ) ∫ a b f ( x ) d x + ∫ a b ∫ c d g ( y ) d y d x = ( b − a ) ∫ c d g ( y ) d y + ∫ c d ∫ c b f ( x ) d x d y .
In the following exercises, the function f is given in terms of double integrals. a. Determine the explicit form of the function f. b. Find the volume of the solid tinder the surface z = f(x. v) and above the region R. C. Find the average value of the function f on R. d. Use a computer algebra system (CAS) to plot z = f(x. y) and z = f a v e in the same system of coordinates. 51. Show that if f and g are continuous on [ a , b ] and [ c , d ], respectively, then ∫ c b ∫ a d [ f ( x ) + g ( y ) ] d y d x = ( d − c ) ∫ a b f ( x ) d x + ∫ a b ∫ c d g ( y ) d y d x = ( b − a ) ∫ c d g ( y ) d y + ∫ c d ∫ c b f ( x ) d x d y .
In the following exercises, the function f is given in terms of double integrals.
a. Determine the explicit form of the function f.
b. Find the volume of the solid tinder the surface z = f(x. v) and above the region R.
C. Find the average value of the function f on R.
d. Use a computer algebra system (CAS) to plot z = f(x. y) and z = favein the same system of coordinates.
51. Show that if
f
and g are continuous on [a,b] and [c,d], respectively, then
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.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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