Find the area of the shaded region. (a) (b 5- (3, 4)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 45E
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Find the area of the shaded region.
(a)
(b)
(3, 4)
4-
у 3
3 y
2
(5, 0)
3.
6.
-2
-2
Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using
precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part
of the problem. First determine the height of the triangle and the length of the triangle's base.
height
units
base
units
STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in
part (a).
square units
STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require
calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded region as
approximately equivalent to a triangle on top of a rectangle and sum the areas of these objects.)
square units
5,
4.
2.
Transcribed Image Text:Find the area of the shaded region. (a) (b) (3, 4) 4- у 3 3 y 2 (5, 0) 3. 6. -2 -2 Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base. height units base units STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a). square units STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded region as approximately equivalent to a triangle on top of a rectangle and sum the areas of these objects.) square units 5, 4. 2.
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