微积分definiteintegralEvaluatethedefiniteintegral.form0toa/19x^37(a^2-x^38)^1/2dx(a>0)

Question

微积分definite integral
Evaluate the definite integral.
form 0 to a/19
x^37 (a^2-x^38)^1/2 dx (a > 0)

Answer 1

= From 0 to a/19 (a^2-x^38)^1/2 d x^38/38
replace x^38 with y,derives
=From 0 to (a/19)^38 (a^2-y)^1/2 d y/38
again replace (a^2-y)^1/2 with z
= 1/38 From a^2 to (a^2-(a/19)^38)^1/2 -2z^2 dz
= - 1/(3*19) From a^2 to (a^2-(a/19)^38)^1/2 d z^3
=- 1/(3*19) [a^6 - a^2-(a/19)^38)^3/2]