Given \int_2^5f(x)dx=17 and \int_2^5g(x)dx=-2, evaluate the following. (a)\int_2^5[f(x)+g(x)]dx

Wotzdorfg

Wotzdorfg

Answered question

2021-06-05

Given 25f(x)dx=17 and 25g(x)dx=2, evaluate the following.
(a)25[f(x)+g(x)]dx
(b)25[g(x)f(x)]dx
(c)252g(x)dx
(d)253f(x)dx

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-06-06Added 99 answers

Step 1
According to the standard rules of definite integrals, we have:
1.ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx
2.abcf(x)dx=cabf(x)dx
Step 2
(a)
25[f(x)+g(x)]dx=25f(x)dx+25g(x)dx=(17)+(2)=15
(b)
25[g(x)f(x)]dx=25g(x)dx25f(x)dx=(2)(17)=19
(c)
252g(x)dx=225g(x)dx=2(2)=4
(d)
253f(x)dx=325f(x)dx=3(17)=51

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