Question

homework 1: 1.1-1.4 review
score: 9/17 answered: 6/13
question 7
if
\\(\int_{-56}^{-43} f(x) dx = 9\\)
and
\\(\int_{-56}^{-43} g(x) dx = 25\\)
and
\\(\int_{-56}^{-43} h(x) dx = 23\\)
what does the following integral equal?
\\(\int_{-56}^{-43} 7f(x) + 4g(x) - h(x) dx = \\)

Explanation:

Step1: Split the integral

$\int_{-56}^{-43} [7f(x) + 4g(x) - h(x)] dx = 7\int_{-56}^{-43} f(x) dx + 4\int_{-56}^{-43} g(x) dx - \int_{-56}^{-43} h(x) dx$

Step2: Substitute given values

$7(9) + 4(25) - 23$

Step3: Calculate each term

$63 + 100 - 23$

Step4: Compute final sum

$63+100=163; 163-23=140$

Answer:

140