Given:
The expression is:

To find:
The integration of the given expression.
Solution:
We need to find the integration of
.
Let us consider,

![[\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x]](https://tex.z-dn.net/?f=%5B%5Cbecause%201%2B%5Ccos%202x%3D2%5Ccos%5E2x%2C1-%5Ccos%202x%3D2%5Csin%5E2x%5D)

![\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Ctan%20%5Ctheta%20%3D%5Cdfrac%7B%5Csin%20%5Ctheta%7D%7B%5Ccos%20%5Ctheta%7D%5Cright%5D)
It can be written as:
![[\because 1+\tan^2 \theta =\sec^2 \theta]](https://tex.z-dn.net/?f=%5B%5Cbecause%201%2B%5Ctan%5E2%20%5Ctheta%20%3D%5Csec%5E2%20%5Ctheta%5D)


Therefore, the integration of
is
.
F(-4)=G(-4) because when the two lines cross over the f line is at the -4 and same with G
Answer:
a. 12s + 19j - 3
36 + 28 - 3 = 61
b.
Shirt (per unit cost):
Before Discount: $12
After Discount: $12 - $3 = $9
Jeans (pair cost):
Before Discount: $19
After Discount: $19 - $3 = $16
(12-3)s + (19-3)j
27 + 32 = $59