### Area Between Curves: Find the area of the region bounded by

```Area Between Curves: Find the area of the region bounded by the
curves y = f (x) and y = g(x).
Area Between Curves: Find the area of the region bounded by the
curves y = f (x) and y = g(x).
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Area Between Curves: Find the area of the region bounded by the
curves y = f (x) and y = g(x).
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Step 2: Find the x-coordinates of the points of intersection. Add these to
the sketch. If necessary make a new sketch.
Area Between Curves: Find the area of the region bounded by the
curves y = f (x) and y = g(x).
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Step 2: Find the x-coordinates of the points of intersection. Add these to
the sketch. If necessary make a new sketch.
Step 3: On the sketch, darkly shade a typical rectangle between x = xi
and x = xi + ∆x. Write down its area, ∆Ai.
Area Between Curves: Find the area of the region bounded by the
curves y = f (x) and y = g(x).
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Step 2: Find the x-coordinates of the points of intersection. Add these to
the sketch. If necessary make a new sketch.
Step 3: On the sketch, darkly shade a typical rectangle between x = xi
and x = xi + ∆x. Write down its area, ∆Ai.
Step 4: Write the area A as a deﬁnite integral, simplify using symmetry if
possible, and evaluate.
Area Between Curves: Find the area of the region bounded by the
curves y = x2 and y = 2x2 − 1.
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Step 2: Find the x-coordinates of the points of intersection. Add these to
the sketch. If necessary make a new sketch.
Step 3: On the sketch, darkly shade a typical rectangle between x = xi
and x = xi + ∆x. Write down its area, ∆Ai.
Step 4: Write the area A as a deﬁnite integral, simplify using symmetry if
possible, and evaluate.
Area Between Curves: Find the area of the region bounded by the
curves y = x2 and y = 2x2 − 1.
Step 1: Draw a rough sketch the two curves and shade the bounded region
between them with vertical lines. Identity the top and bottom function of x.
Step 2: Find the x-coordinates of the points of intersection. Add these to
the sketch. If necessary make a new sketch. Ans: x = ±1.
Step 3: On the sketch, darkly shade a typical rectangle between x = xi
and x = xi + ∆x. Write down its area, ∆Ai. Ans: ∆Ai = (1 − x2i )∆x
Step 4: Write the area A as a deﬁnite
integral, simplify
using symmetry if
∫ 1
∫ 1
possible, and evaluate. Ans: A = −1(1 − x2)dx = 2 0 (1 − x2)dx = 43
```