Part I: Numerical Integration
Evaluate the following integrals:
i. ∫4(1−?−4?3 +2?5)??
0
ii. ∫3(?2??)?? 0
a) Analytically
b) Multiple application of Trapezoidal rule n = 4. c)
Simpson’s 1/3 rule for n = 4.
d) Simpson’s 1/3 and Simpson’s 3/8 rule for n = 5. e)
Determine the true percent relative error.
23. Given a = 5, b = 4, c = 2, evaluate the following:
a) a//c
b) a % b
c) b **c
d) b *= c
27. Given the following
var_1 = 2.0
var_2 = "apple"
var_3 = 'orange'
var_4 = 4
Predict the output of the following statements or indicate that
there would be an error.
a) print (var_1)
b) print (var_2)
c) print ("var_3")
d) print (var_1 / var_4)
e) print (var_4 + var_3)
f) print (var_2...
1) Find the following indefinite integrals.
a) (4-3xsec^2 x)/x dx
b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx
2) A particle starts from rest and moves along the x-axis from
the origin at t = 0 with acceleration
a(t) = 6 - 2t
(ms^-2) at time t. When and where will it come to rest.
Remember dvdt =
acceleration and dsdt = velocity
3) Use substitution to find the following integrals.
a) (9x)/ sqrt...
1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5,
b=3, c=8, d=4
a. 6
b. 3
c. 15/2
d. 17/13
2. Solve for x: 5(x+3) = 35
a. 2
b. 7
c. 4
d. -4
3. Acid rain occurs primarily as a result of
a. operating a nuclear power plant
b. burning coal or oil containing sulfur
c. by-products created by operating an oil refinery
d. the use of Freon and other refrigerants
4. The "ozone holes" at the polar region arise...
Evaluate the following integrals using trigonometric
identities
(a) intergal sin6 x cos3 x dx
(b) Z π/2
o
cos5 x dx
(c) Z
sin3
(
√
x)
√
x
dx
(d) Z
tsin2
t dt
(e) Z
tan2
θ sec4
θ dθ
(f) Z
x sec x tan x dx
(15) Evaluate each of the following integrals. (a) Z cos(x)
ln(sin(x)) dx (b) Z x arcsin(x 2 ) dx (c) Z 1 0 ln(1 + x 2 ) dx (d)
Z 1/4 0 arcsin(2x) dx
(16) Use the table of integrals to evaluate the integrals, if
needed. You may need to transform the integrand first.
(a) Z cos(4t) cos(5t)dt
(b) Z 1 cos3 (x) dx
(c) Z 1 x 2 + 6x + 9 dx
(d) Z 1 50 −...
A, B, C, D are all matricies
A = 2x3
1 2 −3
−1 4 5
,
B = 2x3
3 0 −1
1 2 1
, C = 2x2
2 5
1 2
,
D = 3x3
1 −1 1
2 −1 2
4 −3 4
Find each of the following or explain why it does not exist.
1) A + B,
2) 2A − 3B,
3) A + C,
4) A − C,
5) AC,
6) CA,
7)...