(). 4. (a) Find the length of the curve y = } cosh(2r) from point (r, y) = to (x, y) = cosh 2 Hint: cosh (ar)–sinh?(ax) = 1, (cosh(ax)) = a sinh(ar), –(sinh(ar)) = a cosh(ar). dar (b) Sketch the region of integration and evaluate the repeated integral (2.r + y) dæ dy (c) Reverse the order of integration in the repeated integral in item (b), identify the new integration limits but do not re-evaluate the integral.
(). 4. (a) Find the length of the curve y = } cosh(2r) from point (r, y) = to (x, y) = cosh 2 Hint: cosh (ar)–sinh?(ax) = 1, (cosh(ax)) = a sinh(ar), –(sinh(ar)) = a cosh(ar). dar (b) Sketch the region of integration and evaluate the repeated integral (2.r + y) dæ dy (c) Reverse the order of integration in the repeated integral in item (b), identify the new integration limits but do not re-evaluate the integral.
(). 4. (a) Find the length of the curve y = } cosh(2r) from point (r, y) = to (x, y) = cosh 2 Hint: cosh (ar)–sinh?(ax) = 1, (cosh(ax)) = a sinh(ar), –(sinh(ar)) = a cosh(ar). dar (b) Sketch the region of integration and evaluate the repeated integral (2.r + y) dæ dy (c) Reverse the order of integration in the repeated integral in item (b), identify the new integration limits but do not re-evaluate the integral.
Please solve the vector calculus curve and integration problems. If possible please solve each one
Thank you.
Transcribed Image Text:(n)
4. (a) Find the length of the curve y =
cosh(2r) from point (x, y) =
0.
to
(21, y) = ( 1,
1
- cosh 2
(x,
Hint: cosh? (ax)–sinh²(ax) = 1,
d
:(cosh(ax)) = a sinh(ax),
-(sinh(ax)) = a cosh(a.x).
%3D
dr
de
(b) Sketch the region of integration and evaluate the repeated integral
(2x + y) dæ dy
(c) Reverse the order of integration in the repeated integral in item (b), identify
the new integration limits but do not re-evaluate the integral.
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.
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