05-03-018 The Fundamental Theorem of Calculus
Z x a f(t) dt a≤x≤b is continuous on [a,b] and differentiable on (a,b) and g′(x) = f(x). First, we’ll use properties of the definite integral to make the integral match the form in the Fundamental Theorem. Z 1 sin(x) p 1+t2 dt= −1· Z sin(x) 1 p 1+t2 dt so we have y= − Z sin(x) 1 p 1+t2 dt The minus sign is just a constant factor ... ................
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