Q. 7 - Calculus

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 − ${\int }_{-3}^{2}f\left(x\right)dx$? 

Step-by-Step Solution

Answer

negative

positive

Step1. Given Information

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

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

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

Step2. Answer

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

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