Area and the Definite Integral

Question 1

definite integral

Answer 1

the integral used to find the area between the curve, the x-axis and the given boundaries

Question 2

area of a trapezium

Answer 2

1/2 h(a+b)

a and b are two parallel lengths

Question 3

how to use the trapezoidal rule

Answer 3

b-a/2 (f(a) + f(b))
start by constructing a table of values of the intervals (x) and these plugged into equation (f(x))
plug into formula and add together

Question 4

fundamental theorem of calculus

Answer 4

integral from a to b:

F(b) - F(a): top minus bottom

Question 5

If the numerator of a given quotient is the derivative of the denominator…

Answer 5

the primitive is ln(f(x))

Question 6

regions of curve above x-axis

Answer 6

assigned a + to the area

Question 7

regions of curve below the x-axis

Answer 7

assigned a - to the area

Question 8

If a curve is even, the integral is

Answer 8

2 x the integral from 0 to a point

(find 0–>a area and double it

Question 9

If a curve is odd, the integral is

Answer 9

integral from a–>-a = 0

Question 10

reversing the integral

Answer 10

switch the bounds and put a negative in front

Question 11

area between curves=

Answer 11

integral of top curve minus integral of bottom curve

TOP MINUS BOTTOM

Question 12

sums of areas that intersect=

Answer 12

integral of f(x) from a to intersection + integral of g(x) from intersection to b

Question 13

if you get a negative integral

Answer 13

the area below the x-axis is greater than the area above