ap-calculus-ab 2006 Q5

ap-calculus-ab · USA · free-response_formB Areas by integration Average Value of a Function

Let $R$ be the region in the first quadrant under the graph of $y = \frac { x } { x ^ { 2 } + 2 }$ for $0 \leqq x \leqq$ (a) Find the area of $R \cdot \left( - x - \alpha , \frac { 1 } { 1 } \right)$ (b) If the line $x = k$ divides $R$ into two regions of equal area, what is the value of $k$ ? (c) What is the average value of $y = \frac { x } { x ^ { 2 } + 2 }$ on the interval $0 \leqq x \leqq \sqrt { 6 }$ ?

Let $R$ be the region in the first quadrant under the graph of $y = \frac { x } { x ^ { 2 } + 2 }$ for $0 \leqq x \leqq$
(a) Find the area of $R \cdot \left( - x - \alpha , \frac { 1 } { 1 } \right)$
(b) If the line $x = k$ divides $R$ into two regions of equal area, what is the value of $k$ ?
(c) What is the average value of $y = \frac { x } { x ^ { 2 } + 2 }$ on the interval $0 \leqq x \leqq \sqrt { 6 }$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6