MAT421 - Lab 2



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#%matplotlib notebook
%matplotlib inline
#%pylab inline
#init_session(use_unicode=True)
from __future__ import division
from sympy import *
x, y, z, t = symbols('x y z t', real=True)
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
init_printing()

To run a cell: Shift+Enter.

To print:

Cell > Run All.
Make sure no there is no error.
File -> Print Preview. Print using the browser's print menu.

Print your name using print function.

Example: print("Ali bin Ahmad")



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Print your student id using print function.



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Define the functions f and g, find the intersections (if exists), plot the graph and find the enclosed area.

a) $f(x) = x^2 + 2$ and $g(x)=1-x$ between $x=0$ and $x=1$.

Define $f$ and $g$. Then, plot $f$ and $g$ on the same graph for $x\in[0,1]$.



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Calculate the enclosed area.



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b) $f(x) = x - 1$ and $g(x)=2x^3 - 1$ between $x=1$ and $x=2$.

Define $f$ and $g$. Then, plot $f$ and $g$ on the same graph for $x\in[1,2]$.



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Calculate the enclosed area.



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c) $f(x) = (x-1)^2$ and $g(x)=-x+3$.

Define $f$ and $g$. Then, find the $x$ value of the intersection point(s) of $f$ and $g$ using function "solve".



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Plot $f$ and $g$ on the same graph for $x\in[-1,2]$.



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Calculate the enclosed area.



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Define the functions f and g, find the intersections (if exists), plot the graph and find the volume of solids by DIsk (Washer).

a) $f(x) = \sqrt x$, $g(x) = x - 2$, $y = 0$. Revolve about $y=0$.

Define $f$ and $g$. Then, find the $x$ value of the intersection point(s) of $f$ and $g$ using function "solve".



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Plot $f$ and $g$ on the same graph for $x\in[0,4]$.



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Calculate the volume.



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Define the functions f and g, find the intersections (if exists), plot the graph and find the volume of solids by Cylindrical Shell Method.

a) $f(x) = x^2 + 1$, $g(x)=0$, $x=0$ and $x=2$. Revolve about $x=0$.

Define $f$ and $g$. Then, plot $f$ and $g$ on the same graph for $x\in[0,2]$.



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Calculate the volume.



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The End