## Area between Curves

### 1. Find the area of the region under the graph of \(f\) on \( [a, b]\).
solution

### (a) \( f(x)=x^2-2x+2;\quad [-1, 2] \)

### (b) \(\displaystyle{f(x)= \frac{1}{x^2};\quad [1, 2] }\)

### 2. Use a definite integral to find the area under the curve between the given x-values. solution

### \[f(x)=8x^3, \quad x=2 \: \text{to} \: x=3\]

### 3. Use a definite integral to find the area under the curve between the given x-values. solution

### \[f(x)=\frac{1}{\sqrt{x}}, \quad x=9 \: \text{to} \: x=16\]

### 4. Find the area between the curves \( f(x)=x \) and \(
g(x)=x^2\). solution

### 5. Find the area between the curves \( y=2x-1 \) and \(
y=x^2-1\). solution

### 3. Find the area between the curves as shown.
solution

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