Calculus

Fundamental Theorem of Calculus

Connection of derivative and integral

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f(2.50)A=5.551
b = 2.50
∫02.50f(x) dx=F(2.50)−F(0)=5.5511\int_0^{2.50}f(x)\,dx = F(2.50)-F(0) = 5.5511
\ racddx∫axf(t) dt=f(x)\ rac{d}{dx}\int_a^x f(t)\,dt = f(x)

Fundamental theorem of calculus: the derivative of an integral with moving upper limit = the original function. Area under curve = F(b)-F(a) (evaluate the antiderivative).