Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. ( Note : Some of the problems may he done using techniques of integration learned previously.) 83. ∫ sin 5 x cos 2 x d x
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. ( Note : Some of the problems may he done using techniques of integration learned previously.) 83. ∫ sin 5 x cos 2 x d x
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may he done using techniques of integration learned previously.)
83.
∫
sin
5
x
cos
2
x
d
x
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.
1. Evaluate
(2,5)
(3x+y)dx+(2y-x)dy
(0,1)
(i) along the straight lines from (0, 1) to (2, 1) and then from (2, 1) to (2,5), and (ii)
along the parabola y = x² + 1.
Don't use any Al tool
show ur answer in pe
n and paper then take
Don't use any Al tool
show ur answer in pe
n and paper then take
20. Solve the given system of differential equations:
x' =
x+y, x(0) = 0
y' = 2x,
y(0) = 1
4. Verify the Cauchy-Goursat theorem for the function f(z) =225z around the
closed curve C defined by a half circle || = 1 from the point (1,0) to (-1, 0) in the
counterclockwise direction and then the straight line from (-1,0) to (1,0).
Don't use any Al tool
show ur answer in pe
n and paper then take
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