Expert answers to "Given ∫−17g(x)dx=12,∫−17f(x)dx=18,∫−13g(x)dx=7,∫−14f(x)dx=10 Evaluate ∫574f(x)dx"

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iohanetc

Answered question

2021-09-26

Given $\int_{- 1}^{7} g (x) d x = 12, \int_{- 1}^{7} f (x) d x = 18, \int_{- 1}^{3} g (x) d x = 7, \int_{- 1}^{4} f (x) d x = 10$
Evaluate $\int_{5}^{7} 4 f (x) d x$

Answer & Explanation

grbavit

Skilled2021-09-27Added 109 answers

Step 1
Given function

\int_{- 1}^{7} g (x) d x = 12

...(1)

\int_{- 1}^{7} f (x) d x = 18

...(2)

\int_{- 1}^{3} g (x) d x = 7

...(3)

\int_{- 1}^{4} f (x) d x = 10

...(4)
We have to find

\int_{5}^{7} 4 f (x) d x

We know that

\int_{a}^{b} f (x) = \int_{a}^{c} f (x) + \int_{c}^{b} f (x)

Step 2
Using the given integrals

\int_{5}^{7} 4 f (x) d x = 4 [\int_{- 1}^{7} f (x) d x - \int_{- 1}^{4} f (x) d x]

Substitute the values of given integrals

\int_{5}^{7} 4 f (x) d x = 4 (18 - 10)

\int_{5}^{7} 4 f (x) d x = 4 (8)

\int_{5}^{7} 4 f (x) d x = 32

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