Page 132 - Calculus Demystified

CHAPTER 4
The Integral
119

Fig. 4.20
SOLUTION
On the given interval, sin x ≥ cos x. See Fig. 4.21. Thus the area we wish to
compute is
5π/4
Area = [sin x − cos x] dx
π/4
x=5π/4
=[− cos x − sin x]
x=π/4
√ √
√ √
2 2 2 2
= − − − − − − −
2 2 2 2
√
= 2 2.
y

y = sin x

x
y = cos x

Fig. 4.21

You Try It: Calculate the area between y = sin x and y = cos x, −π ≤ x ≤ 2π.
2
You Try It: Calculate the area between y = x and y = 3x + 4.