difficulty in solving integration of a function

Question

0 个投票

how could I calculate the integeral of a function

F = log(1 + p/[(x(t))^2 + (y(t))^2)]) where t varies from 0 to 7

here

x(t) = 100-(50*cos(theta)*t)

y(t) = H+50*sin(theta)*t-4.9*t^2

theta could be any between 0 to 75 degree

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Jintao Wu 2020-3-2

I can't undrstand the means of ' how could I calculate the intergrral of a function '

Answer 1

Bjorn Gustavsson 2020-3-2

0 个投票

Implement the functions x(t,theta), y(t,theta,H) and F(t,H,p,theta) step-by step. Something like this:

y = @(t,theta,H) H+50*sin(theta)*t-4.9*t.^2; % Note the change to elementwise operation in the last term
...etc

Then Check that your function F is wellbehaved in the intervall of interest:

t = linspace(0,7,701);
plot(t,F(t,1,2,pi/5))

If that looks reasonably OK integrate:

H = 12;
p = 0.012;
theta = pi/7;
Q = integral(@(t) F(t,H,p,theta),0,1);

HTH