Chapter 4: Q. 6 (page 384)

Suppose $f (x) \geq g (x)$ on [1, 3] and $f (x) \leq g (x)$ on (−∞, 1] and [3,∞). Write the area of the region between the graphs of f and g on [−2, 5] in terms of definite integrals without using absolute values .

Short Answer

Expert verified

The area is $\int_{- 2}^{1} (g (x) - f (x)) d x + \int_{1}^{3} (f (x) - g (x)) d x + \int_{3}^{5} (g (x) - f (x)) d x .$

Step by step solution

Step 1. Given Information

It is supposed that $f (x) \geq g (x) on [1, 3] and f (x) \leq g (x) on (- \infty, 1] and [3, \infty) .$

A function f is positive on $(- \infty, - 1]; [2, \infty)$ and negative on $[- 1, 2] .$

The objective is to write the area on $[- 2, 5] .$

The intervals will be $[- 2, 1], [1, 3], [3, 5] .$

Step 2. Area,

The absolute area will be,

$\int_{- 2}^{1} (g (x) - f (x)) d x + \int_{1}^{3} (f (x) - g (x)) d x + \int_{3}^{5} (g (x) - f (x)) d x$

Therefore, the area is $\int_{- 2}^{1} (g (x) - f (x)) d x + \int_{1}^{3} (f (x) - g (x)) d x + \int_{3}^{5} (g (x) - f (x)) d x .$

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Suppose $f (x) \geq g (x)$ on [1, 3] and $f (x) \leq g (x)$ on (−∞, 1] and [3,∞). Write the area of the region between the graphs of f and g on [−2, 5] in terms of definite integrals without using absolute values .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Area,

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Suppose f(x)≥g(x)on [1, 3] and f(x)≤g(x)on (−∞, 1] and [3,∞). Write the area of the region between the graphs of f and g on [−2, 5] in terms of definite integrals without using absolute values .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Area,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

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Study anywhere. Anytime. Across all devices.

Suppose $f (x) \geq g (x)$ on [1, 3] and $f (x) \leq g (x)$ on (−∞, 1] and [3,∞). Write the area of the region between the graphs of f and g on [−2, 5] in terms of definite integrals without using absolute values .