Question

Help me plz!!! Wanna know the answer of (d). Thank you so much!!!!

Answer 1

Answer:

d = -9

Step-by-step explanation:

First lets input our x value for g(x)

This gives us the integral

$g(6) = \int\limits^6_{-4} {f(x)} \, dx$

First, we need to split this integral into the different aspects of the piecewise function. This will give us

$g(6)=\int\limits^0_{-4} {4} \, dx +\int\limits^5_0 {-5} \, dx +\int\limits^6_5 {0} \, dx$

Now, we need to evaluate each of these integrals

$\int\limits^0_{-4} {4} \, dx=4x|\limits^0_{-4}\\\\4(0)-4(-4)=16$

$\int\limits^5_0 {-5} \, dx=-5x|\limits^5_0\\\\-5(5)--5(0)\\\\-25$

$\int\limits^6_5 {0} \, dx=0$

Now all we need to do is add the values of each of these integrals

$16-25=-9$