[T] The transformations T : R P. i = 1,.... 4. defined by T 1 (u.v) = ( u. —v). T 2 , ( u, v ) = (—u. v). T 3 ( u. v ) = (—u. — v ), and T 4 (u. v) = (v. u) are called reflections about the x -axis. y -axis. origin, and the line y = x. respectively. a. Find the image of the region S = {(u. v ) u 2 + — v 2 — 2u - 4v +1 ≤ 0} in the xy- plane through the transformation T 1 ∘ T 2 ∘ T 3 ∘ T 4 b. Use a CAS to graph R. c. Evaluate the Integral ∬ S sin ( u 2 ) d u d v by using a CAS. Round your answer to two decimal places.
[T] The transformations T : R P. i = 1,.... 4. defined by T 1 (u.v) = ( u. —v). T 2 , ( u, v ) = (—u. v). T 3 ( u. v ) = (—u. — v ), and T 4 (u. v) = (v. u) are called reflections about the x -axis. y -axis. origin, and the line y = x. respectively. a. Find the image of the region S = {(u. v ) u 2 + — v 2 — 2u - 4v +1 ≤ 0} in the xy- plane through the transformation T 1 ∘ T 2 ∘ T 3 ∘ T 4 b. Use a CAS to graph R. c. Evaluate the Integral ∬ S sin ( u 2 ) d u d v by using a CAS. Round your answer to two decimal places.
[T] The transformations T : R P. i = 1,.... 4. defined by T1(u.v) = (u. —v). T2, (u, v) = (—u. v). T3 (u. v) = (—u. —v), and T4(u. v) = (v. u) are called reflections about the
x-axis. y-axis. origin, and the line y = x. respectively.
a. Find the image of the region S = {(u. v)u2+ — v2— 2u -4v +1
≤
0} in the xy- plane through the transformation
T
1
∘
T
2
∘
T
3
∘
T
4
b. Use a CAS to graph R.
c. Evaluate the Integral
∬
S
sin
(
u
2
)
d
u
d
v
by using a CAS. Round your answer to two decimal places.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Evaluate V9+x² dx+xy°dy along the positively oriented curve C where the C is the
boundary of the rectangle with vertices (0, 0), (0, 4), (2, 0), and (2, 4).
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