Volume by Slicing - # 2

[Jason76]

The solid lies between planes perpendicular to the x axis at \(\displaystyle x = -1\) and \(\displaystyle x = 1\). The cross-sections perpendicular to the x axis between these planes are squares whose bases run from the semi-circle \(\displaystyle y = -\sqrt{1 - x^{2}}\) to the semi-circle \(\displaystyle y = \sqrt{1 - x^{2}}\)

\(\displaystyle V = \int_{a}^{b} A(x) dx\)

\(\displaystyle x^{2}\) is the area of a square

\(\displaystyle A = x^{2}\)

\(\displaystyle V = \int_{-1}^{1} [2 \sqrt{1 - x^{2}}]^{2}\) On the right track here?

\(\displaystyle V = \int_{-1}^{1} [4 (1 - x^{2})]\)

\(\displaystyle V = \int_{-1}^{1} 4 - 4x^{2}\)

The book says the answer will come out to \(\displaystyle \dfrac{16}{3}\)

 

[Jason76]

The solid lies between planes perpendicular to the x axis at \(\displaystyle x = -1\) and \(\displaystyle x = 1\). The cross-sections perpendicular to the x axis between these planes are squares whose bases run from the semi-circle \(\displaystyle y = -\sqrt{1 - x^{2}}\) to the semi-circle \(\displaystyle y = \sqrt{1 - x^{2}}\)

\(\displaystyle V = \int_{a}^{b} A(x) dx\)

\(\displaystyle x^{2}\) is the area of a square

\(\displaystyle A = x^{2}\)

\(\displaystyle V = \int_{-1}^{1} [x][2 \sqrt{1 - x^{2}}]^{2} dx\)

\(\displaystyle V = \int_{-1}^{1} [x][4 (1 - x^{2})] dx\)

\(\displaystyle V = \int_{-1}^{1} [x][4 - 4x^{2})] dx\)

\(\displaystyle V = \int_{-1}^{1} 4x - 4x^{2})] dx\)

\(\displaystyle V = \dfrac{4x^{2}}{2}- \dfrac{4x^{3}}{3})] \)

\(\displaystyle V = 2x^{2} - \dfrac{4x^{3}}{3})] \)

 

[Deleted member 4993]

Jason,

You do not take our suggestions and insist on going onto your merry-wrong-way. I am not going to respond to your posts - because I feel it is a waste of my precious spare-time.

 

[mmm4444bot]

I agree with Subhotosh. I will no longer be posting in your threads, after this.

Speaking for myself only, I do not think that you are a serious student, and I no longer believe your statements about your "professors".

These boards are not a chat room. I hope that you look elsewhere for help writing your book of step-by-step-by-unnecessary-step "explanations".