Show that the four answers given in Section 1 for ∫ 0 π / 2 d θ / cos θ are all correct. Hints: For the beta function result, use (6.4). Then get the gamma function results by using (7.1) and the various Γ function formulas. For the elliptic integral , use the hint of Problem 17 with α = π / 2 .
Show that the four answers given in Section 1 for ∫ 0 π / 2 d θ / cos θ are all correct. Hints: For the beta function result, use (6.4). Then get the gamma function results by using (7.1) and the various Γ function formulas. For the elliptic integral , use the hint of Problem 17 with α = π / 2 .
Show that the four answers given in Section 1 for
∫
0
π
/
2
d
θ
/
cos
θ
are all correct. Hints: For the beta function result, use (6.4). Then get the gamma function results by using (7.1) and the various
Γ
function formulas. For the elliptic integral, use the hint of Problem 17 with
α
=
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.
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