Question

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

Short answer

negative

positive

Step-by-step solution

Step1. Given Information

$\text{It is supposed that}f\text{is negative on}[-3,2]\text{.}$

$\text{The objective is to determine if}{\int }_{-3}^2 f\left(x\right)dx\text{and}-{\int }_{-3}^2 f\left(x\right)dx\text{will be positive or negative.}$

localid="1649761961973" $\text{Since,}f\text{is negative on}[-3,2]\text{so,}{\int }_{-3}^2 f\left(x\right)dx\text{will also be negative.}$

Step2. Answer

$\text{Now, since}{\int }_{-3}^2 f\left(x\right)dx\text{is negative obviously}-{\int }_{-3}^2 f\left(x\right)dx\text{will be positive.}$

$\text{Therefore, the answers are negative, positive}$.