The net area of the region in relation to the x-axis, is just the integral at those bounds, thus
![\bf \displaystyle \int\limits_{-\frac{\pi }{2}}^{\pi }~8cos(\theta )\cdot d\theta \implies 8\int\limits_{-\frac{\pi }{2}}^{\pi }~cos(\theta )\cdot d\theta \\\\\\ \left. 8sin(\theta )\cfrac{}{} \right]_{-\frac{\pi }{2}}^{\pi }\implies [8sin(\pi )]~-~\left[8sin\left(-\frac{\pi }{2} \right) \right]\implies [0]-[-8]\implies 8](https://tex.z-dn.net/?f=%5Cbf%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%7D%5E%7B%5Cpi%20%7D~8cos%28%5Ctheta%20%29%5Ccdot%20d%5Ctheta%20%5Cimplies%208%5Cint%5Climits_%7B-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%7D%5E%7B%5Cpi%20%7D~cos%28%5Ctheta%20%29%5Ccdot%20d%5Ctheta%0A%5C%5C%5C%5C%5C%5C%0A%5Cleft.%208sin%28%5Ctheta%20%29%5Ccfrac%7B%7D%7B%7D%20%20%5Cright%5D_%7B-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%7D%5E%7B%5Cpi%20%7D%5Cimplies%20%5B8sin%28%5Cpi%20%29%5D~-~%5Cleft%5B8sin%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%20%5Cright%29%20%20%5Cright%5D%5Cimplies%20%5B0%5D-%5B-8%5D%5Cimplies%208)
QUESTION 18
1 answer:
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we are given
step-1: Simplify expression inside parenthesis
we will combine like terms
so, firstly we will take common denominator
step-2: Distribute 1/2 inside
step-3: Combine like terms
We can find common denominator
we can also write it as in mixed form
so, we will get
option-C.............Answer