Question

exercises 1.2 the definite integral
score: 150/170 answered: 15/17
question 16
if (int_{-81}^{-32} f(x) dx = 9) and (int_{-81}^{-32} g(x) dx = 19) and (int_{-81}^{-32} h(x) dx = 20) what does the following integral equal? (int_{-81}^{-32} 5f(x) + 2g(x) - h(x) dx =
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Explanation:

Step1: Split integral using linearity

$$\int_{-81}^{-32} [5f(x)+2g(x)-h(x)]dx = 5\int_{-81}^{-32}f(x)dx + 2\int_{-81}^{-32}g(x)dx - \int_{-81}^{-32}h(x)dx$$

Step2: Substitute given integral values

$$= 5(9) + 2(19) - 20$$

Step3: Calculate each term

$$= 45 + 38 - 20$$

Step4: Compute final sum

$$= 83 - 20$$

Answer:

$63$