MAT 142 Day 6

1331 days ago by kcrisman

The purpose of this worksheet is very simple.  It is to show you how to check your work on indefinite and definite integrals.

The syntax for an indefinite integral is very easy.  Note you do need to provide the variable!  You'll see why in Calculus III.

Here is $\int 2xe^{x^2} dx$

integrate(2*x*e^(x^2), x) 
       
e^(x^2)
e^(x^2)

Notice a few other things.

  • Powers are carets ^ (Shift-6)
  • Multiplication is asterisk * (Shift-8)
    • This is important to avoid ambiguity in our usual notation.
  • The "+C" is implied, not explicit.
  • If I want another variable because the problem has it, I'll need to ask for it.
var('y') integrate(y^3, y) 
       
1/4*y^4
1/4*y^4

If I want a definite integral, I just add the endpoints, separated by commas.  Here is $\int_{-1}^1 2xe^{x^2} dx$.

integrate( 2*x*e^(x^2), x, -1, 1) 
       
0
0

Excellent, just as suspected.

If logging in to use this sheet is too much, of course you can always just paste these commands in the Sage cell server.