(1)计算定积分∫(1/√2~1)√(1-x^2)/x^2 *dx (2)计算定积分∫(-3~0)√(1-x)*dx 求
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(1)计算定积分∫(1/√2~1)√(1-x^2)/x^2 *dx (2)计算定积分∫(-3~0)√(1-x)*dx 求详细过程谢
![(1)计算定积分∫(1/√2~1)√(1-x^2)/x^2 *dx (2)计算定积分∫(-3~0)√(1-x)*dx 求](/uploads/image/z/1160658-18-8.jpg?t=%EF%BC%881%EF%BC%89%E8%AE%A1%E7%AE%97%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%AB%EF%BC%881%2F%E2%88%9A2%7E1%EF%BC%89%E2%88%9A%EF%BC%881-x%5E2%EF%BC%89%2Fx%5E2+%2Adx+%EF%BC%882%EF%BC%89%E8%AE%A1%E7%AE%97%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%AB%EF%BC%88-3%7E0%EF%BC%89%E2%88%9A%EF%BC%881-x%EF%BC%89%2Adx+%E6%B1%82)
∫(1/√2->1)√(1-x^2)/x^2 *dx
= -[1/x+x](1/√2->1)
= √2 +1/√2 - 2
= (3/2)√2 -2
∫(-3->0)√(1-x)*dx
= - (2/3) [(1-x)^(3/2)] (-3->0)
=-(2/3)( 1-8)
=7/3
再问: =-(2/3)( 1-8) =7/3 是不是应该等于14/3啊?
再答: 是14/3
= -[1/x+x](1/√2->1)
= √2 +1/√2 - 2
= (3/2)√2 -2
∫(-3->0)√(1-x)*dx
= - (2/3) [(1-x)^(3/2)] (-3->0)
=-(2/3)( 1-8)
=7/3
再问: =-(2/3)( 1-8) =7/3 是不是应该等于14/3啊?
再答: 是14/3
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