Chapter 4: Q. 7 (page 384)

If f is negative on [−3, 2], is the definite integral $\int_{- 3}^{2} f (x) d x$ positive or negative? What about the definite integral − $\int_{- 3}^{2} f (x) d x$ ?

Short Answer

Expert verified

negative

positive

Step by step solution

Step1. Given Information

$It is supposed that f is negative on [- 3, 2] .$

$The objective is to determine if \int_{- 3}^{2} f (x) d x and - \int_{- 3}^{2} f (x) d x will be positive or negative.$

localid="1649761961973" $Since, f is negative on [- 3, 2] so, \int_{- 3}^{2} f (x) d x will also be negative.$

Step2. Answer

$Now, since \int_{- 3}^{2} f (x) d x is negative obviously - \int_{- 3}^{2} f (x) d x will be positive.$

$Therefore, the answers are negative, positive$ .

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If f is negative on [−3, 2], is the definite integral $\int_{- 3}^{2} f (x) d x$ positive or negative? What about the definite integral − $\int_{- 3}^{2} f (x) d x$ ?

Short Answer

Step by step solution

Step1. Given Information

Step2. Answer

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If f is negative on [−3, 2], is the definite integral $\int_{- 3}^{2} f (x) d x$ positive or negative? What about the definite integral − $\int_{- 3}^{2} f (x) d x$ ?