Use the formula to find the area under the curve y = sin x

Chapter 5, Problem 85E

(choose chapter or problem)

Use the formula

\(\sinh +\sin 2 h+\sin 3 h+\cdots+\sin m h=\frac{\cos (h / 2)-\cos ((m+(1 / 2) h)}{2 \sin (h / 2)}\)

to find the area under the curve \(y=\sin x\) from \(x=0\) to \(x=\pi / 2\) in two steps:
a. Partition the interval \([0, \pi / 2]\) into \(n\) subintervals of equal length and calculate the corresponding upper sum \(U\); then
b. Find the limit of \(U\) as \(n \rightarrow \infty\) and \(\Delta x=(b-a) / n \rightarrow 0\).

Equation Transcription:

Text Transcription:

sinh + sin2h + sin3h +...+ sinmh =cos(h/2)-cos((m+(1+2))h)/2sin(h/2)

y=sinx

x=0

x=pi/2

[0, pi/2]

n

U

U

n right arrow infinity

delta x=(b-a)/n right arrow 0