Let and be integrable on such that and Find the value of .

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

Problem

Let

f

and

g

be integrable on

[-3,4]

such that

\displaystyle \int_{-3}^{1} f(x)\,dx = 5,\quad \int_{1}^{4} f(x)\,dx = -2,\quad \int_{-3}^{4} g(x)\,dx = 8,

and

\displaystyle \int_{1}^{4} [f(x)+g(x)]\,dx = 1.

Find the value of

\displaystyle \int_{-3}^{1} g(x)\,dx

. (a)

11

(b)

5

(c)

-5

(d)

3