急问(高等微积分)Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.b.Using the First Fundamental Theorem (Integrating Derivatives).注:上下
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![急问(高等微积分)Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.b.Using the First Fundamental Theorem (Integrating Derivatives).注:上下](/uploads/image/z/14601044-20-4.jpg?t=%E6%80%A5%E9%97%AE%28%E9%AB%98%E7%AD%89%E5%BE%AE%E7%A7%AF%E5%88%86%29Let+a+and+b+be+positive+numbers.Find+the+value+of+%E2%88%AB%5Bax%2Bb%5Ddx+in+the+following+two+ways%3Aa.Using+elementary+geometry%2Cinterpreting+%E2%88%AB%5Bax%2Bb%5Ddx+as+an+area.b.Using+the+First+Fundamental+Theorem+%28Integrating+Derivatives%29.%E6%B3%A8%3A%E4%B8%8A%E4%B8%8B)
急问(高等微积分)Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.b.Using the First Fundamental Theorem (Integrating Derivatives).注:上下
急问(高等微积分)
Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:
a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.
b.Using the First Fundamental Theorem (Integrating Derivatives).
注:上下界皆为 1 ,0
急问(高等微积分)Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.b.Using the First Fundamental Theorem (Integrating Derivatives).注:上下
a)使用面积原理,直线在(0,1)下的图形为梯形,面积为
∫[ax+b]dx =(1/2)*(b+a+b)*1=(1/2)(a+2b)
b)积分
∫[ax+b]dx =(1/2)ax^2+bx在0到1上计算=(1/2)a+b=(1/2)(a+2b)
a.直线y=ax+b与x轴所围图形,其中0《x《1