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Antiderivatives and Areas - SolutionsMath 125In this worksheet, we explore the Fundamental Theorem of Calculus and applications of the AreaProblem to problems involving distance and velocity.FTC Practice1Letf(x) be given by the graph to the right and defineA(x) =integraldisplayx0f(t)dt. Compute the following.A(1) =2A(2) =4A(3) =612A(4) =9A′(1) =2A′(2) =2A′(3) =3A′(4) =2The maximum value ofA(x) on the interval [0,5] is1012The maximum value ofA′(x) on the interval [0,5] is312321345y=f(x)Velocity and Distance2A toy car is travelling on a straight track. Its velocityv(t), in m/sec, be given by the graph to the right. Defines(t)to be the position of the car in meters. Choose coordinatesso thats(0) = 0. Compute the following.123