(a) State the rule that relates the indefinite integral of the sum (or difference) of…
MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
(a) State the rule that relates the indefinite integral of the sum (or difference) of two real-valued functions to the individual indefinite integrals of those functions.
(b) Let f(x)=2x and g(x)=sinx. Evaluate ∫[f(x)+g(x)]dx as a single integral and also evaluate ∫f(x)dx+∫g(x)dx. Differentiate each antiderivative obtained and show explicitly that both derivatives give the same original integrand.
(c) When you integrate a sum of several functions, why is only one constant of integration written in the final answer even though each separate integral could have its own constant? Give a brief justification.