## Area of regions between curves

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

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

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

## 1. Find the area under the curve \( y=x\) on the interval \( [0,4]\). solution

## 2. Find the area of the region bounded by the curve \(f(x)=3x-x^2, \) and the \(x\)-axis. solution

## 3. Find the area of the region bounded by the curves \(y=\sqrt{x}, x=5\) and the \(x\)-axis. solution

## 4. Find the area of the region bounded by the curves:
\( y=x^3 \) and \( y= x \). solution

## 5. Find the area of the region bounded by the curves: \( y=x^2 \) and
\( y=4x-x^2\). solution

## 6. Find the area of the region bounded by the curves: \( y=\sqrt{x}\)
and \(
y=x^2\). solution

## 7. Find the area of the region bounded by the curves: \( y=\sqrt{x},
y=x^2\) and \(x=2\). solution

## 8. Compute the area of the region bounded by the curves \( y^2=x \)
and \( y=2-x\). solution

## 9. Find the area of the region bounded by the curves:
\( x=y^2 \) and \( x=8-y^2\). solution

## 10. Find the area of the region bounded by the curves \(y=\sec ^{2} x, \: y=6 \cos x, \, \, -\pi / 4 \leq x \leq \pi / 4 \). solution

## 11. Find the area bounded by the curves \(y=e^x\) and \(y=x e^{x^2}\) between \(x=0\) and \(x=1\). solution

## 12. Draw the region bounded by the curves, and find its area. \( y = 3/x, \, y=12x, \, y=x/3, \, x \ge 0.\) solution

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