How to apply integral on a vector?
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Hello,
I have a problem that I can't find the right answer to.
I have these equations:
y = x ^ 2 ;
z = ∫ y dx = ∫ x^2 dx = 1/3 * x^3;
In Matlab code, let's consider two vectors:
x = -20 : 1 : 20 ;
y = x . * x ;
z = ∫ y dx ; which we already know the answer to, that is: z = x . * x . * x * 1/3;
I would like to calculate the vector z with some command without the need to create a function, as I do not own Symbolic Math Toolbox, or any other Toolbox needed.
Can someone help me with this? Maybe write the corresponding code that goes with it?
Thank You in advance.
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Nikhil Yewale
le 8 Mai 2020
1) Using function handle without specifying explicity whole array
a = -20; b = 20; % lower limit a, upper limit b
y = @(x) x.^2; % create fuction handle of x , followed by function definition
I = integral(y,a,b); % required answer
2) With whole array x.. You may check that required integral is same by both methods
dx = 0.01; % increment in x array
X = a:dx:b; %array X
cumulative_I = dx*cumtrapz(X.^2); % evaluates cumulative integral using traezoidal method
II = cumulative_I(end); % required answer
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