In Problems 4 to 13, identify each of the integrals as an elliptic integral (see Examples 1 and 2 ). Learn the notation of your computer program (see Problem 3 ) and then evaluate the integral by computer. ∫ − π / 2 3 π / 8 d θ 1 − 9 10 sin 2 θ
In Problems 4 to 13, identify each of the integrals as an elliptic integral (see Examples 1 and 2 ). Learn the notation of your computer program (see Problem 3 ) and then evaluate the integral by computer. ∫ − π / 2 3 π / 8 d θ 1 − 9 10 sin 2 θ
In Problems 4 to 13, identify each of the integrals as an elliptic integral (see Examples 1 and 2 ). Learn the notation of your computer program (see Problem 3 ) and then evaluate the integral by computer.
∫
−
π
/
2
3
π
/
8
d
θ
1
−
9
10
sin
2
θ
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.
Suppose that a friend
of yours has decided to solve a certain integral using trigonometric
substitution. As a first step, she draws the following triangle.
Question 2
3
Based on this picture, express
x,
dx,
and
the length of the remaining third side
in terms of the chosen angle 0.
Question 3.4. Determine the following integrals
15x2
dr
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