Maple Lab number 1 - Done in class on 2/18/2016 - due on 2/25/2016
Name:
Instructions: For each function below do the following. Feel free to work with a partner on this
assignment.
(a) (Without Maple) Write down the best method to use to compute the indefinite integral of
the function. Write your answer down.
(b) (Without Maple) Compute an indefinite integral of the function. Write your answer down.
Write our answer in the space provided. Please use pencil.
(c) (With Maple) Differentiate your answer to (a). If your answer doesn’t match the original
function, go back to step (a).
(The best way to check with Maple is to take your answer, differentiate it, subtract that from
your original function, and then ask Maple to simplify.)
R
Example: Let a(x) = cos2 (x). To integrate a(x), write a(x) = 1+cos(2x)
. Then a(x) dx =
2
R 1
R
dx + cos(2x)
dx = x2 + sin(2x)
+ C.
2
2
4
To get Maple to check this, type simplify(diff(x/2 + sin(2*x)/4,x)-cos(x)^2). Maple
should return zero.
1. b(y) = sin(y) cos(y)3 .
2. c(z) = z tan(z)2 .
1
2
3. d(m) = m4 sin(2m).
4. e(t) = ln(t +
2
√
t2 − 1).
r −2r−1
5. f (r) = (r−1)
2 (r 2 +1) . You can get Maple to compute a partial fraction decomposition with a
command like convert(r/(r^2 - 2r -3),parfrac).
3
6. g(s) =
√
1 + 4s2 .
7. h(w) =
8. i(v) =
w2 −3w+7
.
(w2 −4w+6)2
v2
.
v 6 +3v 3 +2
(Again, feel free to use Maple to do the partial fraction decomposition.)
4
9. j(θ) =
1
.
1+cos(θ)
10. k(τ ) =
τ ln(τ )
√
.
τ 2 −1