AP Calculus AB 微积分 积分

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AP Calculus AB 微积分 积分
 

1D2不知道.

[a..b] ∫ f(x) dx = a+2b
[a..b] ∫ (f(x)+3) dx
=[a..b] ∫ f(x) dx + [a..b] ∫ 3 dx
=a+2b+ 3x | [a..b]
=a+2b+3b-3a
=5b-2a
(D) is the correct answer.
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[a..b] ∫ f(x) dx = a+2b
[a..b] ∫ (f(x)+3) dx
=[a..b] ∫ f(x) dx + [a..b] ∫ 3 dx
=a+2b+ 3x | [a..b]
=a+2b+3b-3a
=5b-2a
(D) is the correct answer.
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The Riemann Sum is given by the general formula:
sum(f(x[i])*(b-a)/n, i=1..n);
In this question, a=0, b=1, n=20, f(x)=√(x/20)
sum(√(x[i]/20))*(1-0)/20, i=1..n)
=1/20 * [√(1/20)+√(2/20)+...+√(20/20)]
So, (C) is the right answer.

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