**INTEGRAL HARD Calculus problem forever?**

*The function r (t) represents the rate at which a country's debt is growing. Consider* the following expressions: The function r (t) represents the rate at which a country's debt is growing. Consider the following expressions: A. ∫ 19892001r '(T) dt B. [R (2001)-r (1989) / 2.001 to 1.989] C. r (2001)-r (1989) D. r (2001) E. ∫ 19892001r (t) dt _________________________________ and interpretations: A. Average rate change in debt between 1989 and 2001 B. Change in the rate of debt between 1989 and 2001 C. Increase in debt between 1989 and 2001 D. The country's debt in 2001 E. Change debt in 2001 to determine whose interpretation corresponds to that expression. Note that can not be one to one correspondence between all the expressions and interpretations. This is what I have (looks like I'm wrong) someone please explain: expression = d = a = b = expressionB expressionC expressionD expression e = c

Expression Expression c = d = r (t) represents a rate which is the derivative of debt r (t) = d '(t) if integrated r (t) as in the expression E, is debt [area] under the curve between the two years. Thus E is the interpretation of D, and therefore an expression must go with c by default.

**The Hardest Part of Calculus**