Area B/w Curves: y=(secx)^2/4 & 4(cosx)^2

[brickair]

Determine the area between:

1.) y=((secx)^2)/4 and y=4(cosx)^2

2.) y=e^x , y=e^-4x , and x=ln4

3.) y=5cosx and y=5cos(2x) for 0≤x≤pi

 

[mathmari]

Determine the area between:

1.) y=((secx)^2)/4 and y=4(cosx)^2

2.) y=e^x , y=e^-4x , and x=ln4

3.) y=5cosx and y=5cos(2x) for 0≤x≤pi

The area between $y=f(x)$ and $y=g(x)$ on the interval $[a,b]$, when $f(x) \geq g(x)$ is euqal to $\displaystyle{\int_a^bf(x)-g(x) dx}$.

Can you apply this in your case?

 

[MarkFL]

Determine the area between:

1.) y=((secx)^2)/4 and y=4(cosx)^2

2.) y=e^x , y=e^-4x , and x=ln4

3.) y=5cosx and y=5cos(2x) for 0≤x≤pi

Hello and welcome to MHB!

Just for future reference, we ask that you:

a) Post no more than two questions per thread in your initial post. Follow-up questions are fine, but if you have a new question, please begin a new thread.

b) Show what you have tried, as this gives our helpers a better idea where you are stuck and how best to help. Our goal here is to maximize the learning for the person asking the question by getting them involved in the solution process.