The rate of depreciation of a building is given by D'(t) = 4000(20 − t) dollars per year, 0 ≤ t ≤ 20; see the following figure. A coordinate plane is given. The horizontal axis is labeled t and the vertical axis is labeled D'(t). A line and a shaded region are graphed. The line labeled D'(t) starts at (0, 80000), goes down and right, passes through (10, 40000), and stops at t = 20 on the positive t-axis. The area under the line from t = 0 to t = 10 is shaded. (a) Use the graph to find the total depreciation of the building over the first 10 years (t = 0 to t = 10). $ (b) Use the definite integral to find the total depreciation over the first 10 years.$
The rate of depreciation of a building is given by D'(t) = 4000(20 − t) dollars per year, 0 ≤ t ≤ 20; see the following figure. A coordinate plane is given. The horizontal axis is labeled t and the vertical axis is labeled D'(t). A line and a shaded region are graphed. The line labeled D'(t) starts at (0, 80000), goes down and right, passes through (10, 40000), and stops at t = 20 on the positive t-axis. The area under the line from t = 0 to t = 10 is shaded. (a) Use the graph to find the total depreciation of the building over the first 10 years (t = 0 to t = 10). $ (b) Use the definite integral to find the total depreciation over the first 10 years.$
The rate of depreciation of a building is given by D'(t) = 4000(20 − t) dollars per year, 0 ≤ t ≤ 20; see the following figure. A coordinate plane is given. The horizontal axis is labeled t and the vertical axis is labeled D'(t). A line and a shaded region are graphed. The line labeled D'(t) starts at (0, 80000), goes down and right, passes through (10, 40000), and stops at t = 20 on the positive t-axis. The area under the line from t = 0 to t = 10 is shaded. (a) Use the graph to find the total depreciation of the building over the first 10 years (t = 0 to t = 10). $ (b) Use the definite integral to find the total depreciation over the first 10 years.$
The rate of depreciation of a building is given by D'(t) = 4000(20 − t) dollars per year, 0 ≤ t ≤ 20; see the following figure.
A coordinate plane is given. The horizontal axis is labeled t and the vertical axis is labeled D'(t). A line and a shaded region are graphed.
The line labeled D'(t) starts at (0, 80000), goes down and right, passes through (10, 40000), and stops at t = 20 on the positive t-axis.
The area under the line from t = 0 to t = 10 is shaded.
(a) Use the graph to find the total depreciation of the building over the first 10 years
(t = 0
to
t = 10).
$
(b) Use the definite integral to find the total depreciation over the first 10 years. $
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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