Which of the following correctly expresses in terms of separate integrals of and ?

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Which of the following correctly expresses ∫ab(5f(x)−2g(x)) dx\displaystyle\int_a^b \bigl(5f(x)-2g(x)\bigr)\,dx in terms of separate integrals of ff and gg? (a) 5∫baf(x) dx−2∫bag(x) dx5\displaystyle\int_b^a f(x)\,dx - 2\displaystyle\int_b^a g(x)\,dx (b) ∫abf(x) dx+∫abg(x) dx\displaystyle\int_a^b f(x)\,dx + \displaystyle\int_a^b g(x)\,dx (c) 5∫abf(x) dx−2∫abg(x) dx5\displaystyle\int_a^b f(x)\,dx - 2\displaystyle\int_a^b g(x)\,dx (d) 15∫abf(x) dx−12∫abg(x) dx\tfrac15\displaystyle\int_a^b f(x)\,dx - \tfrac12\displaystyle\int_a^b g(x)\,dx

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