Determine whether the statement is true or false If it is tr

Determine whether the statement is true or false. If it is true, explain why. If it is false explain why or give an example that disproves the statement.

Solution

integral ( x= b to x = a)f(x) dx is not always positive

it depends on the function and upper bound and the lower bound

take f(x) = x and b = -5 and a = 1

so we will get integral ( x= b to x = a)f(x) dx = integral ( x dx)

                                                                  = x^2/2 from ( -5 to 1)

                                                                 = 1 - ( 25) / 2 = -24/2 = -12

so it is false