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If f is negative on [−3, 2], is the definite integral ∫-32f(x)dx positive or negative? What about the definite integral − ∫-32f(x)dx?

Short Answer

Expert verified

negative

positive

Step by step solution

01

Step1. Given Information

It is supposed thatfis negative on[−3,2].

The objective is to determine if∫−32 f(x)dxand−∫−32 f(x)dxwill be positive or negative.

localid="1649761961973" Since,fis negative on[−3,2]so,∫−32 f(x)dxwill also be negative.

02

Step2. Answer

Now, since∫−32 f(x)dxis negative obviously−∫−32 f(x)dxwill be positive.

Therefore, the answers are negative, positive.

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