MHB 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

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