a, evaluate the definite integral: 2 to 3 x2/square
root of x3-7 dx
b, Determine the indefnite integral :
12x5-5x/x2 dx
c, Evaluate the integral : 10x sin (2x+3) dx
d, Evaluate the integral: 1/x2 square root of
36-x2 dx
Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}.
(a) Prove that U is a subspace of F4.
(b) Find a basis for U and prove that dimU = 2.
(c) Complete the basis for U in (b) to a basis of F4.
(d) Find an explicit isomorphism T : U →F2.
(e) Let T as in part (d). Find a linear map S: F4 →F2 such that
S(u) = T(u) for all u ∈...
Evaluate the following integral using trigonometric
substitution. a) find the partial decomposition of the integrand b)
evaluate the indefinite integral
1. 6/x(x^2+2)^2
2. 5/x(x^2+1)^2?
6. Let A = {1, 2, 3, 4} and B = {5, 6, 7}. Let f = {(1, 5),(2,
5),(3, 6),(x, y)} where x ∈ A and y ∈ B are to be determined by
you. (a) In how many ways can you pick x ∈ A and y ∈ B such that f
is not a function? (b) In how many ways can you pick x ∈ A and y ∈
B such that f : A → B...
Evaluate the integral: ∫√36x^2−49 / x^3 dx
(A) Which trig substitution is correct for this integral?
x=49/36sec(θ)
x=7/6sec(θ)
x=1/36sec(θ)
x=6/7sec(θ)
x=7/6sin(θ)
(B) Which integral do you obtain after substituting for
xx?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?
Note: WAMAP does not recognize the inverse secant (arcsec)
function. You will need to...
Evaluate the integral: ∫−14 / x^2√x^2+100 dx
(A) Which trig substitution is correct for this integral?
x=−14sec(θ)
x=100sec(θ)
x=10tan(θ)
x=100sin(θ)
x=10sin(θ)
x=100tan(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?
. Let U be a non-empty set. For A and B subsets of U, define the
relation A R B if an only if A is a proper subest of B. a. Is R
reflexive? Prove or explain why not. b. Is R symmetric? Prove or
explain why not c. Is R transitive? Prove or explain why not. d. Is
R antisymmetric? Prove or explain why not. e. Is R an equivalence
relation? Prove or explain why no
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