a. Sketch the region of integration, D, for which y=√x (4x+10y) dA= (4x+10y) dy dx. y=? 2-0 y=z b. Determine the equivalent iterated integral that results from integrating in the opposite order (dx dy, instead of dy dx). That is, determine the limits of integration for which y=? (4x+10y) dA= (4x + 10y) de dy. 7² c. Evaluate one of the two iterated integrals above. Explain what the value you obtained tells you. d. Set up and evaluate a single definite integral to determine the exact area of D, A(D). e. Determine the exact average value of f(x, y) = 4x+10y over D.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Activity 11.3.3. Consider the iterated integral (4x+10y) dy dx.
a. Sketch the region of integration, D, for which
y=√x
2=0
y=x
y=x
(4x+10y) da = -12 (4x+10y) dy dx.
b. Determine the equivalent iterated integral that results from integrating in
the opposite order (dx dy, instead of dy da). That is, determine the limits
of integration for which
(4x + 10y) dA= (4x + 10y) dx dy.
da
y=? x=?
c. Evaluate one of the two iterated integrals above. Explain what the value
you obtained tells you.
d. Set up and evaluate a single definite integral to determine the exact area
of D, A(D).
e. Determine the exact average value of f(x, y) = 4x+10y over D.
Transcribed Image Text:Activity 11.3.3. Consider the iterated integral (4x+10y) dy dx. a. Sketch the region of integration, D, for which y=√x 2=0 y=x y=x (4x+10y) da = -12 (4x+10y) dy dx. b. Determine the equivalent iterated integral that results from integrating in the opposite order (dx dy, instead of dy da). That is, determine the limits of integration for which (4x + 10y) dA= (4x + 10y) dx dy. da y=? x=? c. Evaluate one of the two iterated integrals above. Explain what the value you obtained tells you. d. Set up and evaluate a single definite integral to determine the exact area of D, A(D). e. Determine the exact average value of f(x, y) = 4x+10y over D.
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