The answer is (d) 7/2======we have
we also have an integral
notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:
notice that for the piecewise function f, the function has the equationf(x) = x when x ≤ 0. so for the integral
, f(x) = x so it changes into
for the piecewise function f, the function has the equationf(x) = x+1 when x > 0. for the integral
, we have
therefore, back to our splitted integral: