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.

Fluid Force on an Isoceles Trapezoid

A vertical gate in a dam has the shape of an isoceles trapezoid. The top of the gate measures 10 feet across, the gate is 11 feet below the surface of the water, the gate is 7 feet high, the bottom of the gate is 8 feet across. Find the fluid force on the gate.

Coordinates of a centroid of a plane region

NOTE: I need to see how to find the centroid coordinates by using integrals and moments. I have attached a word document w/ the formulas we are supposed to use to find the centroid. Now here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region.

Fluid force - Applications of Integration

NOTE: We are supposed to find the fluid force using integrals. I have attached a word document with the fluid force formula we are supposed to use. Please use the US system of measurement (i.e. pounds) Now here is the problem: A vertcial gate in a dam has the shape of an isoceles trapezoid. The top of the gate measures 10 ...continues

Spring compression using Hooke's law: Find the work done by compressing the spring an additional 2 inches.

A 1,000 lb force compresses a spring 5 inches from its natural length of 20 inches. Find the work done by compressing the spring an additional 2 inches.