Question

∫r^5*√（a²-r²）dr这个积分怎么算的

Answer 1

用三角代换,设r=a*sin(t),被积函数变为a^5*[sin(t)]^5*cos(t)

∫r^5*√（a²-r²）dr=a^5∫[sin(t)]^5d(sin(t))