Question

求解高数积分问题

Answer 1

希望可以帮到你。

Answer 2

∫ (-1->1) (1-x^2)^(5/2) dx
=∫ (-1->1) (1-x^2)^(5/2) dx
=[x.(1-x^2)^(5/2)]|(-1->1) + 5∫ (-1->1) x^2. (1-x^2)^(3/2) dx
=0 +5∫ (-1->1) x^2. (1-x^2)^(3/2) dx
=-5∫ (-1->1) (1-x^2). (1-x^2)^(3/2) dx +5∫ (-1->1) (1-x^2)^(3/2) dx
6∫ (-1->1) (1-x^2)^(5/2) dx =5∫ (-1->1) (1-x^2)^(3/2) dx
∫ (-1->1) (1-x^2)^(5/2) dx
=(5/6)∫ (-1->1) (1-x^2)^(3/2) dx
=(5/6)(3/4)∫ (-1->1) (1-x^2)^(1/2) dx
=(5/8)∫ (-1->1) (1-x^2)^(1/2) dx
=(5/4)∫ (0->1) (1-x^2)^(1/2) dx
=(5/4)∫ (0->π/2) (cosu )^2 du
=(5/8)∫ (0->π/2) (1+cos2u ) du
=(5/8)(π/2)
=(5/16)π