Q. 6 Suppose f(x)鈮(x)聽on [1, 3] a... [FREE SOLUTION]

Chapter 4: Q. 6 (page 384)

Suppose $f (x) 鈮� g (x)$ on [1, 3] and $f (x) 鈮� g (x)$ on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�2, 5] in terms of definite integrals without using absolute values .

Short Answer

Expert verified

The area is ${鈭�}_{鈭� 2}^{1} 鈥� (g (x) 鈭� f (x)) d x + {鈭�}_{1}^{3} 鈥� (f (x) 鈭� g (x)) d x + {鈭�}_{3}^{5} 鈥� (g (x) 鈭� f (x)) d x .$

Step by step solution

Step 1. Given Information

It is supposed that $f (x) 鈮� g (x) on [1, 3] and f (x) 鈮� g (x) on (鈭� 鈭�, 1] and [3, 鈭�) .$

A function f is positive on $(鈭� 鈭�, 鈭� 1]; [2, 鈭�)$ and negative on $[鈭� 1, 2] .$

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,

${鈭�}_{鈭� 2}^{1} 鈥� (g (x) 鈭� f (x)) d x + {鈭�}_{1}^{3} 鈥� (f (x) 鈭� g (x)) d x + {鈭�}_{3}^{5} 鈥� (g (x) 鈭� f (x)) d x$

Therefore, the area is ${鈭�}_{鈭� 2}^{1} 鈥� (g (x) 鈭� f (x)) d x + {鈭�}_{1}^{3} 鈥� (f (x) 鈭� g (x)) d x + {鈭�}_{3}^{5} 鈥� (g (x) 鈭� f (x)) d x .$

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Suppose $f (x) 鈮� g (x)$ on [1, 3] and $f (x) 鈮� g (x)$ on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�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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91影视

Suppose f(x)鈮�g(x)on [1, 3] and f(x)鈮�g(x)on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�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

Calculus

Applied Mathematics

Decision Maths

Geometry

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose $f (x) 鈮� g (x)$ on [1, 3] and $f (x) 鈮� g (x)$ on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�2, 5] in terms of definite integrals without using absolute values .