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Chapter 5: Q. 80 (page 418)

Consider the function f(x)=4xe-x2.

(a) Find the signed area of the region between the graph of f(x)and the x-axis on [-1,2]shown here:

(b) Find the absolute area of the same region.

Short Answer

Expert verified

Part (a) The value is -2e-4-e-1.

Part (b) The area is2e-4-e-1.

Step by step solution

01

Part (a) Step 1. Given information.

The given function isf(x)=4xe-x2.

02

Part (a) Step 2. Explanation.

According to the given question,

the integral will be,

鈭�-124xe-x2dx=4鈭�-12xe-x2dx=-2鈭�-1-4eudu=-2ew-1-4=-2e-4-e-1

03

Part (b) Step 1. Explanation.

The absolute area will be,

|A|=-2e-4-e-1=2e-4-e-1

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