How do I integrate cosine to an odd power of 3 or higher?

The steps for integrating cosine to an odd power of 3 or higher are shown using the example Scos^5(x)dx.

How do I integrate sec^3(x)? (or sec to a higher odd power)

The steps for integrating sec^3(x) are shown with explanations.

How do I integrate sin or cos to an even power greater than 2?

The steps for integrating sin or cos to an even power greater than 2 are shown using the example Ssin^4(x)dx.

Functions : Critical Values

The function f(x)=2x^3 - 33x^2 + 108x - 6 has two critical numbers. The smaller one equals ______ and the larger one equals______.

Please explain the process of U substitution.

The steps of U substitution are explained using the example Ssec(2x)tan(2x)dx.

Please explain the process of U substitution.

The steps of U substitution are explained using the example Scos^5(3x)sin(3x)dx.

Use the Washer Method to find volume

Given: f(x)=2x, g(x)=x, x=5 a)Sketch the plane region bounded by the functions graphs b)Use the washer method to find the volume of the solid formed by revolving the above plane region about the x-axis.

shell method to find volume

Given: f(x)=2x, g(x)=10 a)Sketch the plane region bounded by the functions graphs and the y-axis b)Use the shell method to find the volume of the solid formed by revolving the above plane region about the y-axis. NOTE: the graph I did is attached. The answer I got was 523.599. I'm trying to check to see if I did the gr ...continues

Finding the area of the surface from revolving around the x-axis

Given: y = -x^2 + 4x defined on the closed domain [0,4] a) sketch the graph b) Revolve the graph about the x-axis. Find the area of the surface obtained.

Centroid of a plane region

Given: y = 9 - x^2, y = 2 a)sketch the plane region bounded by the functions graph b)Find the coordinates of the centroid of the above plane region.