what is the area of the curve f(x)=sinx with the points of (-n,2) and (n/2,0)?My brother said he would give me one hunted dollars if I completed this with the correct answer, but I only have...

what is the area of the curve f(x)=sinx with the points of (-n,2) and (n/2,0)?

My brother said he would give me one hunted dollars if I completed this with the correct answer, but I only have completed Geometry and I don'tremember doing this at all.

Expert Answers
sciencesolve eNotes educator| Certified Educator

Supposing that you hould evaluate the area enclosed by the curve f(x)=sin x and x axis, hence, you need to evaluate the definite integral `int_(-n)^(n/2) sin x dx`  such that:

`int_(-n)^(n/2) sin x dx = -cos x|_(-n)^(n/2) `

`int_(-n)^(n/2) sin x dx = -cos(n/2) - cos(-n)`

You should remember that the cosine function is even, hence `cos(-n) = cos n` , such that:

`int_(-n)^(n/2) sin x dx = -cos(n/2) - cos n`

Hence, evaluating the area enclosed by the curve `f(x)=sin x`  and x axis yields `int_(-n)^(n/2) sin x dx = -cos(n/2) - cos n.`

kaitieh | Student

0.o you realize that that just went over my head? Now I definitely know that I haven't done this. I haven't taken math since Dec. 2011

I don't understand the curvy symbol on the left with the two numbers on it... or is that just to signify what the hay you're talking about? Like the slanted Ls for angles? And the whole n thing I know it's the variable thing but how do you put it in a scientific calculator?