Question

If the definite integral between [0,x] of f(t)dt=e^(3x)cos(x)+c, what is the value of c?

Answer 1

If f(t)dt=e^(3x)cos(x)|0 to x then using the Fundamental Theorem of calculus you get f(t)dt=[e^(3x)cos(x)+c]-[e^(0)*cos(0)+c]=e^3x*cos(x)-1+(c-c)=e^3x*cos(x)-1. The definite integral doesn't have a constant simply because the c cancels when you subtract.

Answer 2

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Answer 3

I think you can simply find the answer by setting x=0 , you will find c=-1