# AP Calculus 1.1 Integrals

AP Calculus: Integrals Drill 1, Problem 1. What must necessarily be true about this function F(x)?

AP Calculus | Integrals |

Language | English Language |

MPAC 1 | Reasoning with definitions and theorems |

MPAC 2 | Connecting concepts |

MPAC 6 | Communicating |

### Transcript

on the interval 0 acts for an act that is

any real number What must necessarily be true about this

function f of x here the potential answers through so

this question is asking us about the function capital of

acts given lower case k f events All right so

how are these two f thing is related Well we're

told upfront capital f of x area under the curve

lower days f of x which looks exactly like the

definition of an integral which means that capital f of

x is the integral of lower case fx So now

let's start looking at our answer choices starting with anson

choice a is capital f of x discontinuous this one

seems a little tricky so we're going to take the

easy way out and look at the next answer First

we can always come back We'll just leave a trail

Of breadcrumbs Just kidding Start looking at answer choice b

from the fundamental theorem of calculus way know that wherever

fx is continuous the derivative of its integral f of

x is fx Give a little f attacks is this

continuous The derivative isn't even defined since the lower case

fx discontinuous it negative bod and for be truth But

from this logic then we know that choice d is

exactly what we've already concluded that the derivative isn't toe

find a negative five and four for the answer is

d thank goodness no need to go back to joyce

et justus Well those birds already got her pregnant well