Consider the area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant. (a) set up the definite integral needed to find the area. (b) make an appropriate substitution

The required area is

The appropriate Substitution is

Given that,

The area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant.

We have to find,

Set up the definite integral needed to find the area.

Make an appropriate substitution.

According to the question,

The area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant.

The area under one arch is given by,

The required area is

Then,

Then,

The required integral is ,

The appropriate Substitution is .

To know more about Integration click the link given below.

link

has a period of , which is to say one "arch" of the curve occurs over the interval .

a. Then the area under one such arch is

b. Substitute , so that . When , ; when , .

Then the integral is

step-by-step explanation: