Problem

Find the areas bounded by the indicated curves. $…

Problem 16 Easy Difficulty

Find the areas bounded by the indicated curves.
$$y=x, y=3-x, x=0$$

Answer

$$A=\frac{9}{4}$$

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Calculus 2 / BC

Basic Technical Mathematics with Calculus

Chapter 26

Applications of Integration

Section 2

Areas by Integration

Discussion

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Video Transcript

we want to find the area bounded by the curves, Y equals x, Y equals three minus x and x equals zero. This question is challenging your understanding of applications of integration. In particular. It's challenging our ability to find the area between curves. Remember that the area between two curves is for vertical components equals integral A to B, Y tu minus Y, one D X. Or horizontal components A equal integral C two D x x, y Y. To solve this problem. What we're going to do is we're going to sketch this out that way. We can more easily identify the bounds and the curves to make sure answer is correct. So we have Y equals X and Y equals X marked the intersecting X equals 1.5 in the area should have been yellow is bounded by our three curves. Thus we see that if we simply integrate three minus x minus x. From 0 to 1.5, we can solve so from 0 to 3 half three minutes, x minus x is three minutes to x. D x or three x minus x squared from 03 halfs give solution 9/4

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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