Suppose int_(-2)^2 f(x)dx=4,int_2^5 f(x)dx=3, int_(-2)^5 g(x)dx=2.

Suman Cole

Suman Cole

Answered question

2021-05-14

Suppose 22f(x)dx=4,25f(x)dx=3,25g(x)dx=2.
Is the following statement true?
52f(x)dx=3

Answer & Explanation

Alix Ortiz

Alix Ortiz

Skilled2021-05-15Added 109 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,
52f(x)dx=25f(x)dx=3
True Statement

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