MATH/CMSC 206 - Introduction to Matlab
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Symbolic Integration
Contents
Indefinite Integrals
Suppose you'd like to integrate the function 7/(1+x^2). Hmmm.... that reminds me of something I've seen before, but I can't recall the formula... Something about an inverse trig function... Ah, let's just ask Matlab:
int(7/(1 + x^2))
ans = 7*atan(x)
Oh, yeah -- that's it! Matlab uses atan for arctangent which is the same as inverse tangent.
Definite Integrals
Suppose we'd like to compute the area under the curve f(x) = x^3 + ln x over the interval where x is between 5 and 10. Just pass those end-points to the int command as two additional parameters:
int(x^3 + log(x), 5, 10)
ans = 5*log(20) + 9355/4
Self-Test
- Have Matlab integrate the function f(x) = sqrt(x^2 + 3). Aren't you glad we didn't ask you to do this one by hand?
- Have Matlab compute the definite integral of that same function over the interval [2, 4]. Ouch.