d f(t) dt = ? dac a Of(a) OF(x)-F(a) OF(X) Of( x ) Of ( t )An antiderivative of a function f(x) is a function F(x) such that for each x in the domain of f, ... OF(x) - f(x) = constant OF(x) computes the area under the curve of f(x) OF' (x) = f(x)b d (f(x)) dac = a dx Of(b)-f(a) O a constant OF(b)-F(a) OF(x) Of(x)A function f has a family of anti-derivatives. Each member of this family differs by... O constant exponent. O addition of a constant. O multiplication of a constant. O nothing, there is only one anti-derivative of f.Here is a coordinate axis with three functions graphed. Match the graph to the function. Graph 1 Graph 2 Graph 3 Graph 1 a. y= / f(t)dt Graph 2 - v Graph 3 d b. y= Jac (f (2) ) c. y=f(x)Let v(t) measure the velocity of an object along a straight line measured in miles per hour. The integral 1 / v(t) dt measures the O total distance the object travelled by the object from t=a to t=b. O displacement of the object from t=a to time t=b. pb On the other hand, (v(t) | represents the speed of the object, and so lv(t) |dt measures the a O total distance the object travelled by the object from t=a to t=b. O displacement of the object from t=a to time t=b.Classify the following types of objects represented by the symbols: f(t) at represents O a function O a family of functions O a number / f(t) dt represents O a number O a family of functions O a function d dx f (t)dt represents O a number O a function O a family of functions