# Thread: Volume of revolution and integration

1. ## Volume of revolution and integration

a) Find the volume of the solid formed when the area bounded by the curve y = 1/(3x+4), the coordinate axes and the line x=2 is rotated one complete revolution about the x-axis.
b) Evaluate the integral of f(x) between 3 and -3
WHEN f(x) = x+1 (when x<1) and f(x) = 2x (when x >(and equal to) 1)
I am unsure how to complete these two questions, any help is greatly appreciated, thank you

2. Originally Posted by christina a) Find the volume of the solid formed when the area bounded by the curve y = 1/(3x+4), the coordinate axes and the line x=2 is rotated one complete revolution about the x-axis.
b) Evaluate the integral of f(x) between 3 and -3
WHEN f(x) = x+1 (when x<1) and f(x) = 2x (when x >(and equal to) 1)
I am unsure how to complete these two questions, any help is greatly appreciated, thank you
to a): The rotation volume with the x-axis as axis of rotation is calculated by:

$\displaystyle V_{rot} = \int_a^b(\pi \cdot y^2)dx$

In your case a = 0 and b = 2

To determine the integral use integration by substitution with

$\displaystyle u = 3x+4$ which will give $\displaystyle \frac{du}{dx}=3$

After some simplifications you should come out with $\displaystyle V=\frac{\pi}{20}$

to b) Are you asked to calculate the area between the x-axis and the graph of the function or do you want to evaluate the integral.

In the first case you have to split the domain into 3 parts.
In the second case you have to split the domain into 2 parts.

Draw a sketch of the graph and you'll see why these preparations are necessary.

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