INTEGRATION OF TRIGONOMETRIC FUNCTIONS WORKSHEET

Compute each of the following integrals.

Problem 1 :

∫ sin x dx

Solution

Problem 2 :

∫ cos 5x dx

Solution

Problem 3 :

∫ cos x sin4x dx

Solution

Problem 4 :

∫ csc2 x dx

Solution

Problem 5 :

∫ tan x dx

Solution

Problem 6 :

∫ cot x dx

Solution

Problem 7 :

∫ sec x dx

Solution

Problem 8 :

∫ csc x dx

Solution

Problem 9 :

sin2 x dx

Solution

Problem 10 :

sin3 x dx

Solution

Problem 11 :

tan3 x dx

Solution

Problem 12 :

sin 7x cos 3x dx

Solution

Problem 13 :

sin 10x sin 4x dx

Solution

Answer Key

1)   -cos x + C 

2)  (1/5) sin 5x + C

3)  (1/5) sin5x + C

4)   -cot x + C

5)  - In|cos x| + C

6)   In|sin x| + C

7)  In|sec x + tan x| + C

8)  - In|csc x + cot x| + C

9)  (1/2)x - (1/4) sin 2x + C

10)  -cos x + cos3x + C

11)  (1/2) sec2x + ln |cos x| + C

12)  (-1/20) cos 10x - (1/8) cos 4x + C

13)  (1/12) sin 6x - (1/28) sin 14x + C

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