Integration_Trigonometry_Flashcards

Question 1

What is the integral of sin(x) with respect to x?

Answer 1

-cos(x) + C

Question 2

What is the integral of cos(x) with respect to x?

Answer 2

sin(x) + C

Question 3

What is the integral of tan(x) with respect to x?

Answer 3

ln|sec(x)| + C

Question 4

What is the integral of csc(x) with respect to x?

Answer 4

-ln|csc(x) + cot(x)| + C

Question 5

What is the integral of sec(x) with respect to x?

Answer 5

ln|sec(x) + tan(x)| + C

Question 6

What is the integral of cot(x) with respect to x?

Answer 6

ln|sin(x)| + C

Question 7

What is the integral of sin^2(x) with respect to x?

Answer 7

x/2 - sin(2x)/4 + C
Hint: Use the identity cos(2x) = 1 - 2sin^2(x)

Question 8

What is the integral of cos^2(x) with respect to x?

Answer 8

sin(2x)/4 + x/2 + C
Hint: Use the identity cos(2x) = 2cos^2(x) - 1

Question 9

What is the integral of tan^2(x) with respect to x?

Answer 9

tan(x) - x + C
Hint: Use the identity tan^2(x) = sec^2(x) - 1

Question 10

What is the integral of csc^2(x) with respect to x?

Answer 10

-cot(x) + C

Question 11

What is the integral of sec^2(x) with respect to x?

Answer 11

tan(x) + C

Question 12

What is the integral of cot^2(x) with respect to x?

Answer 12

-cot(x) - x + C
Hint: Use the identity cot^2(x) = csc^2(x) - 1