Fundamental Theorem of Calculus (FTC)

Author: John J Weber III, PhD Corresponding Textbook Sections:

Calculus I Rules

NOTE: You are not permitted to use this table on any Assessment.

FunctionDerivativeFunctionAntiderivative
f(x)f(x)f(x)F(x)
f(x)=a; aRf(x)=0f(x)=a; aRF(x)=ax+C
f(x)=axn;
a,nR
f(x)=naxn1f(x)=axn;
a,nR, n1
F(x)=xn+1n+1+C
f(x)=ln(x)f(x)=1xf(x)=1x=x1F(x)=ln(x)+C
f(x)=logb(x);
b>0,b1, x>0
f(x)=1xln(b)f(x)=1xln(b);
b>0,b1
F(x)=(1ln(b))ln(x)+C
f(x)=ax;
a>0,a1
f(x)=ln(a)axf(x)=ax;
a>0,a1
F(x)=axln(a)+C
f(x)=exf(x)=exf(x)=exF(x)=ex+C
f(x)=sin(x)f(x)=cos(x)f(x)=cos(x)F(x)=sin(x)+C
f(x)=cos(x)f(x)=sin(x)f(x)=sin(x)F(x)=cos(x)+C
f(x)=tan(x)f(x)=sec2(x)f(x)=sec2(x)F(x)=tan(x)+C
f(x)=cot(x)f(x)=csc2(x)f(x)=csc2(x)F(x)=cot(x)+C
f(x)=sec(x)f(x)=sec(x)tan(x)f(x)=sec(x)tan(x)F(x)=sec(x)+C
f(x)=csc(x)f(x)=csc(x)cot(x)f(x)=csc(x)cot(x)F(x)=csc(x)+C
f(x)=sin1(x)f(x)=11x2f(x)=11x2F(x)=sin1(x)+C
f(x)=cos1(x)f(x)=11x2f(x)=11x2F(x)=cos1(x)+C
f(x)=tan1(x)f(x)=11+x2f(x)=11+x2F(x)=tan1(x)+C
f(x)=cot1(x)f(x)=11+x2f(x)=11+x2F(x)=cot1(x)+C
f(x)=sec1(x)f(x)=1xx21f(x)=1xx21F(x)=sec1(x)+C
f(x)=csc1(x)f(x)=1xx21f(x)=1xx21F(x)=csc1(x)+C

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Created: Tuesday, 25 August 2020 02:28 EDT Last Modified: Last Modified: Monday, 10 January 2022 - 05:58 (EST)