For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the y-axis. 25. x = sin y , x = cos ( 2 y ) , y = π / 2 , and y = − π / 2
For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the y-axis. 25. x = sin y , x = cos ( 2 y ) , y = π / 2 , and y = − π / 2
For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the y-axis.
25.
x
=
sin
y
,
x
=
cos
(
2
y
)
,
y
=
π
/
2
,
and
y
=
−
π
/
2
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.
(8) (12 points)
(a) (8 points) Let C be the circle x² + y² = 4. Let
F(x, y) = (2y + e²)i + (x + sin(y²))j.
Evaluate the line integral
JF.
F.ds.
Hint: First calculate V x F.
(b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux
integral
√(V × F)
F).dS.
Justify your answer.
Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle.
a = 13, b = 15, C = 68°
Law of Sines
Law of Cosines
Then solve the triangle. (Round your answers to four decimal places.)
C = 15.7449
A = 49.9288
B = 62.0712
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(4) (10 points) Evaluate
√(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV
where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z.
Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY