Mathematics

Mathematics

Problem

Consider two antiderivatives of

\dfrac{dy}{dx}=\cos x

:

F(x)=\displaystyle\int_{0}^{x}\cos t\,dt

and

G(x)=2+\displaystyle\int_{\pi/2}^{x}\cos t\,dt

. Which constant should be added to

F(x)

so that it represents the same function as

G(x)

for all

x

? a) Add 2 to

F(x)

. b) Add 1 to

F(x)

. c) Make no change to

F(x)

. d) Subtract 1 from

F(x)

.

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