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how to implement this Integrate[x^n E^(x - 1), {x, 0, 1}] in matlab

hi I've search and read but I couldn't solve this one in matlab. please help me out to solve this problem integral_0^1 x^n e^(x-1) dx

Solution

  • Generally, you can use different approaches to calculate the required integral:

    1) Symbolic Toolbox --> I'd go for this one because of considerations on n

    syms x n;

f = x.^n.*exp( x - 1 );

int(f,0,1)

    2) quad, integral functions

    g = @(n) (integral(@(x) x.^n.*exp(x-1),0,1));
g = @(n) (quad(@(x) x.^n.*exp(x-1),0,1));

    Then you can evaluate the result depending on n.

    3) trapz function

    x = 0:.001:1;
y = x.^n.*exp( x - 1 );
trapz(x,y)

    But, in this specific case, the calculation of the integral is driven by the exponent n.

    Since I suppose and assume that you know how the integral of 'x.^n' behaves for different n, I will skip the discussion.