The syntax for integrals is roughly the same as that for derivatives.
int=integral(sin(x),0,1)
print 'int = ', int
plot(int)
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Sage evaluates indefinite integrals with the constant set to zero.
integral(sin(x))
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Sage can also handle multiple integrals.
x,y=var('x'),var('y')
integral(integral(5*x*y^2,x,y,2*y),y,0,1)
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We can do multiple integrals in multiple steps as well.
x,y=var('x'),var('y')
innerint=integral(5*x*y^2,x,y,2*y); innerint
outerint=integral(innerint,y,0,1); outerint
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We can also easily do improper integrals.
integral(1/(1+x^2),0,infinity)
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