Question

2. (a) (10 points) Find the leading term of the asymptotics of the following integral for ? ? ?: $I(?) = \int_0^? \cos(?x^2 - x)dx$. Describe the location of the stationary point of the integrand, and the approxima- tion you used for the integrand in its vicinity. (b) (5 points) Use a Computer Algebra System to plot on the same graph the nu- merical value of the integral and your approximation for $16 ? ? ? 1024$. Use logarithmic x-axis. Attach a printout of your CAS session. The expected graph is shown in Fig. 2. Figure 2: Expected result in Problem 2 (solid line asymptotics, dashed line numerically evaluated inte- gral).

          2. (a) (10 points) Find the leading term of the asymptotics of the following integral for
? ? ?:
$I(?) = \int_0^? \cos(?x^2 - x)dx$.
Describe the location of the stationary point of the integrand, and the approxima-
tion you used for the integrand in its vicinity.
(b) (5 points) Use a Computer Algebra System to plot on the same graph the nu-
merical value of the integral and your approximation for $16 ? ? ? 1024$. Use
logarithmic x-axis. Attach a printout of your CAS session.
The expected graph is shown in Fig. 2.
Figure 2: Expected result
in Problem 2 (solid line
asymptotics, dashed line
numerically evaluated inte-
gral).

2. (a) (10 points) Find the leading term of the asymptotics of the following integral for
? ? ?:
I(?) = ∫0^? cos(?x^2 - x)dx.
Describe the location of the stationary point of the integrand, and the approxima-
tion you used for the integrand in its vicinity.
(b) (5 points) Use a Computer Algebra System to plot on the same graph the nu-
merical value of the integral and your approximation for 16 ? ? ? 1024. Use
logarithmic x-axis. Attach a printout of your CAS session.
The expected graph is shown in Fig. 2.
Figure 2: Expected result
in Problem 2 (solid line
asymptotics, dashed line
numerically evaluated inte-
gral).

Added by Brianna W.

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