A sketch of the solid whose volume is given by the iterated integral is shown in the image attached below.
How to calculate an integral?
In this exercise, you're required to sketch the solid whose volume is given by the iterated integral below. Thus, we would first of all evaluate the integral so as to get a unit value.
Given the following integral:
∫¹₀∫₀¹(4 - x - 2y)dxdy
Integrating x with respect to y, we have:
∫¹₀∫₀¹(4 - x - 2y)dxdy = ∫¹₀[(4 - (1/2)- 2y)]dy
∫¹₀∫₀¹(4 - x - 2y)dxdy = 4y - (y/2) - (2y²/2)|¹₀
Evaluating the integral, we have:
∫¹₀∫₀¹(4 - x - 2y)dxdy = 4(1) - (1/2) - (2(1)²/2)
∫¹₀∫₀¹(4 - x - 2y)dxdy = 4 - 1/2 - 1
∫¹₀∫₀¹(4 - x - 2y)dxdy = 5/2
In conclusion, a sketch of the solid whose volume is given by the iterated integral is shown in the image attached below.
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