∫1/(根号下9一X^2)dX

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/22 10:33:58
∫1/(根号下9一X^2)dX∫1/(根号下9一X^2)dX∫1/(根号下9一X^2)dX∫√(9-x^2)dx令x=3sintdx=3costdt√(9-x^2)=3cost原式=∫3cost*3c

∫1/(根号下9一X^2)dX
∫1/(根号下9一X^2)dX

∫1/(根号下9一X^2)dX
∫√(9-x^2)dx
令x=3sint dx=3cost dt
√(9-x^2)=3cost
原式=∫3cost *3cost dt
=9∫cos^2 t dt
=9/2∫(cos2t +1) dt
=9/2∫cos2t dt +9/2∫dt
=9sin2t /4 +9t/2 +C
自己代回来吧