CB.Calc.CHA-4.E: Determine net change using definite integrals in applied contexts.

Determine net change using definite integrals in applied contexts.

Example Problems

Rain is falling with an intensity of

0.8 + 0.4 \sin t

centimeters per hour (where

t

is the number of hours after a storm starts).

How many centimeters of rain fall between

t = 0

and

t = 3\pi/2

?

A vehicle consumes fuel at a rate of

0.1s + 2

liters per kilometer (where

s

is the distance traveled in kilometers since fueling).

How many liters of fuel are used while the vehicle travels from

s = 0

to

s = 20

?

A metal object is cooling, losing thermal energy at a rate of

15e^{-0.3t}

joules per minute (where

t

is the number of minutes since cooling began).

Approximately how many joules of heat are lost between

t = 2

and

t = 10

?

1-on-1 AI tutoring aligned to CB.Calc.CHA-4.E. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.