A function satisfies the differential equation and the graph of passes through the point .

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

A function

y=f(x)

satisfies the differential equation

\dfrac{dy}{dx}=e^{2x}-3

and the graph of

f

passes through the point

(0,4)

. (a) Find the general antiderivative of

e^{2x}-3

and state it in terms of an arbitrary constant. (b) Determine the particular formula for

f(x)

that is consistent with the given point. (c) Evaluate

f(\ln 2)

and interpret the meaning of this value in the context of the function.