Question

select the correcr values if the area in square units of the region under the curve of the function f(x)=3x-1 on the interval [a,4] where a<4 is 12 square units identify all the possible values of a

Answer 1

Step 1: Problem

select the correct values if the area in square units of the region under the curve of the function f(x)=3x-1 on the interval [a,4] where a<4 is 12 square units identify all the possible values of a ​.

Step 2: Concept

$\begin{gathered} \text{Area under the curve f(x) = 3x - 1 on the interval }\mleft\lbrace a,\text{ 4 }\mright\rbrace \\ =\text{ }\int ^4_a\text{ f(x) }dx \end{gathered}$

Step 3: Method

$\begin{gathered} \text{Area under the curve f(x) = }\int ^4_a(3x\text{ - 1) }dx \\ Integrate\text{ the function.} \\ 12\text{ = (}\frac{3x^2}{2}\text{ - x )} \\ 12(2)=3x^2\text{ - 2(x)} \\ 24=3x^2\text{ - 2x} \\ 3x^2\text{ - 2x - 24 = 0} \end{gathered}$