Integration

Question 1

Antiderivative/Indefinite Integral

Answer 1

F is an antiderivative of f on an interval I, if F’(x) = f(x) for all x in I

Question 2

∫f(x)dx= F(x) + C

Answer 2

f(x) is the Integrand
dx is the Variable of Integration
F(x) is the Antiderivative of x
C is the Constant of Integration

Question 3

Integration is the opposite of…

Answer 3

Differentiation

Question 4

Differentiation is the opposite of…

Answer 4

Integration

Question 5

∫ (0) dx = ?

Answer 5

C

Question 6

∫ (k) dx = ?

Answer 6

kx + C

Question 7

∫ kf(x) dx = ?

Answer 7

k ∫ f(x) dx

Question 8

∫ [f(x) ± g(x)] dx = ?

Answer 8

∫ f(x) dx ± ∫ g(x) dx

Question 9

∫ x^n dx = ?

Answer 9

{[x^(n + 1)] / n + 1}, n ≠ -1

Question 10

∫ cos(x) dx = ?

Answer 10

sin(x) + C

Question 11

∫ sin(x) dx = ?

Answer 11

-cos(x) + C

Question 12

∫ sec^2(x) dx = ?

Answer 12

tan(x) + C

Question 13

∫ sec(x) tan(x) dx = ?

Answer 13

sec(x) + C

Question 14

∫ csc^2(x) dx = ?

Answer 14

-cot(x) + C

Question 15

∫ csc(x) cot(x) dx = ?

Answer 15

-csc(x) + C

Question 16

Inscribed Rectangles

Answer 16

Rectangles that lie within/under the curve of a function

Question 17

Circumscribed Rectangles

Answer 17

Rectangles that extend outside/go above the curve of a function

Question 18

How to find Average Area under a Curve

Answer 18

Find the area under the curve and then divide by the range of the domain

Question 19

Fundamental Theorem of Calculus

Answer 19

∫(b to a) f(x)dx = F(x) (b to a) = F(b) - F(a)

Question 20

Mean Value Theorem

Answer 20

∫(b to a) f(x) dx = f(c)(b - a), there is a number c between [a,b] which is a rectangle whose area is equal to the area under the curve

Question 21

Second Fundamental Theorem of Calculus

Answer 21

(d/dx) [ ∫(x to a) f(t) dt ] = f(x)

Question 22

Net Change Theorem

Answer 22

∫(b to a) F’(x) dx = F(b) - F(a)