Suppose \int_{-2}^{2}f(x)dx=4,\int_{2}^{5}f(x)dx=3, \int_{-2}^{5}g(x)dx=2

e1s2kat26

e1s2kat26

Answered question

2021-05-03

Suppose 22f(x)dx=4,25f(x)dx=3,25g(x)dx=2.
Is the following statement true?
f(x)g(x) on the interval 2x5

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2021-05-04Added 104 answers

Step 1
Given:
22f(x)dx=4
25f(x)dx=3
25g(x)dx=2
Step 2
Using properties of Definite Integrals:
ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx
acf(x)dx+cbf(x)dx=abf(x)dx   [c(a,b)]
abf(x)dx=baf(x)dx
Step 3
Now,
25f(x)dx=22f(x)dx+25f(x)dx=4+3=7
25g(x)dx=2
On interval 2x5
f(x)g(x)
False Statement

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