Download cos(x) + C

TRIGONOMETRIC INTEGRALS
Trig Integral Formulas from Derivative Formulas:
Z
•
sin(x)dx = − cos(x) + C;
Z
•
cos(x)dx = sin(x) + C;
Z
•
Z
•
sec2(x)dx = tan(x) + C;
csc2(x)dx = − cot(x) + C;
Z
•
sec(x) tan(x)dx = sec(x) + C;
Z
•
csc(x) cot(x)dx = − csc(x) + C;
Trig Integral Formulas from Substitutions:
Z
• tan(x)dx = − ln(| cos(x)|) + C;
Z
•
cot(x)dx = ln(| sin(x)|) + C;
TRIG INTEGRAL EXAMPLES
Trigonometric Integral Examples
Z
• (sin(2x) + 2 cos(3x))dx?
Z
•
Z
x cos(x2)dx?
1
ex sin(ex)dx?
•
0
Z
•
0
π
4
cos(x)
dx?
1 − sin(x)
π
2
Z
•
π
4
Z
•
TRIG INTEGRAL EXAMPLES
cos(x)
dx?
3
sin (x)
π
| sin(2x)|dx?
0
• If N (t) = 183.55 sin(.0172t − 1.329) + 728.12 is
minutes/day of daylight, find total daylight for 1 year.
183.55 sin(.0172 t−1.329)+728.12
950
900
850
800
750
700
650
600
550
0
50
100
150
200
t
250
300
350