Question

Find the exact value of the area under one arch of the curve y(t) = V0sin(wt). Assume V0 and w are positive constants. You can use V_0 for V0. Note - V is upper case here

Answer 1

y=asin(wt)
Now we find the period, and we know that half a period is an arch.

Answer 2

The period of y=sin(t) is 2pi, so what would y=sin(wt) be?

Answer 3

@Ldaniel

Answer 4

t/w

Answer 5

2pi/w

Answer 6

Alright, then we know that we want to integrate the function from 0 to pi/w, right?

Answer 7

@Ldaniel

Answer 8

yes\

Answer 9

So, we are looking for \[\int\limits_{0}^{pi/w}asin(wt)dt\]

Answer 10

where a and w are both constants.

Answer 11

take out the a, and it becomes \[a \int\limits_{0}^{pi/w}\sin(wt) dt\]