5 Steps to a 5 AP Calculus BC 2019

266 STEP 4. Review the Knowledge You Need to Score High

Trapezoidal Approximations

Another method of approximating the area under a curve is to use trapezoids. See

Figure 12.2-5.

a = x 0 x 1 x 2 b = x 3

y

0 x

f(x)

Figure 12.2-5

Formula for Trapezoidal Approximation

Iff is continuous, the area under the curve off fromx=atox=bis:

Area≈

b−a

2 n

[

f(x 0 )+ 2 f(x 1 )+ 2 f(x 2 )+···+ 2 f(xn− 1 )+f(xn)

]

.

Example

Find the approximate area under the curve of f(x)=cos

(

x

2

)

fromx=0tox=π,

using 4 trapezoids. (See Figure 12.2-6.)

0

1

4

x 2

2 34 π

x

y

f(x) = cos( (

ππ π

Figure 12.2-6

Sincen=4,Δx=

π− 0

4

=

π

4

.