Fundamental theorem of calculus
The fundamental theorem of calculus is:
$\int_a^b f(x) \, \mathrm{d}x = F(b) - F(a)$
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Remember
The fundamental theorem of calculus
- is used in the calculation of definite integrals.
- connects the definite with the indefinite integral.
- represents the connection between differential and integral calculus.
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Hint
The constant of integration $C$ is omitted when subtracting the antiderivatives:
$(F(b)+C)-(F(a)+C)$ $=F(b)-F(a)$
$(F(b)+C)-(F(a)+C)$ $=F(b)-F(a)$