Unit 6

Question 1

Area of a trapezoid?

Answer 1

(y1+y2) * Δx/2

Question 2

Antiderivative of sin(x)

Answer 2

-cos(x)+C

Question 3

Antiderivative of cos(x)

Answer 3

sin(x)+C

Question 4

Antiderivative of sec^2 (x)

Answer 4

tan(x)+C

Question 5

Antiderivative of sec(x)tan(x)

Answer 5

sec(x)+C

Question 6

Antiderivative of csc(x)cot(x)

Answer 6

-csc(x)+C

Question 7

Antiderivative of csc^2 (x)

Answer 7

-cot(x)+C

Question 8

Antiderivative of 1 / (1+x^2)

Answer 8

arctan(x)+C

Question 9

Antiderivative of 1 / (abs(x)*(sqrt(x^2 - 1))

Answer 9

arcsec(x)+C

Question 10

Antiderivative of a^x

Answer 10

( (a^x) / ln(a) ) + C

Question 11

Antiderivative of e^x

Answer 11

e^x + C

Question 12

Antiderivative of 1/x

Answer 12

ln(abs(x)) + C

Question 13

Antiderivative of 0

Answer 13

C

Question 14

integral of du / (a^2 + u^2)

Answer 14

(1/a) * arctan(u/a) + C

Question 15

integral of du / sqrt(a^2 - u^2)

Answer 15

arcsin(u/a) + C

Question 16

integral of du / abs(u)*sqrt(u^2 - a^2)

Answer 16

(1/a) arcsec(u/a) + C

Question 17

integral of du/u

Answer 17

ln(abs(u)) + C

Question 18

What should you remember about MRAM, LRAM, and RRAM, with equal length subintervals?

Answer 18

You can factor out Δx

Question 19

When approximating with LRAM, RRAM, MRAM, and the trapezoid rule, remember to…

Answer 19

use a wavy equals sign to signify when something is approximated

Question 20

Riemann sum notation?

Answer 20

See notes. (makes more sense than as a flashcard).

Question 21

Steps you sometimes forget?

Answer 21

Breaking apart fractions into sums when possible.
Including constants in with u.
+C on the end of indefinite integral.
Basic arithmetic, forgetting steps, numbers, and signs.
Adding dx to the end of an integral.
1/x^n = x^(-n)

Question 22

Mistakes you sometimes make?

Answer 22

Breaking apart the denominator.
Not fully resolving ‘x’ when using u substitution.
-1/2 + 1 = 1/2 not -3/2
Improperly

Question 23

Mistakes you sometimes make?

Answer 23

Breaking apart the denominator.
Not fully resolving ‘x’ when using u substitution.
-1/2 + 1 = 1/2 not -3/2

Question 24

In a Riemann sum, what is delta x?

Answer 24

(b-a)/n