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If f and g are functions such that (picture)
what is the value of (picture)
-12
-3
3
12

This question is designed to be answered without a calculator. If f and g are functions-example-1

1 Answer

9 votes

Given that


\displaystyle \int_0^2 f(x) \, dx = 2


\displaystyle \int_0^2 f(x) - 2g(x) \, dx = 8

we use the linearity of the definite integral to solve for


\displaystyle \int_0^2 g(x) \, dx

We have


\displaystyle \int_0^2 f(x) - 2g(x) \, dx = \int_0^2 f(x) \, dx - \int_0^2 2g(x) \, dx


\displaystyle \int_0^2 f(x) - 2g(x) \, dx = \int_0^2 f(x) \, dx - 2 \int_0^2 g(x) \, dx

Then using the given known integrals,


\displaystyle 8 = 2 - 2 \int_0^2 g(x) \, dx \implies \int_0^2 g(x) \, dx = \boxed{-3}

User Natschz
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