If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3 xf(x^2)

Nannie Mack

Nannie Mack

Answered question

2021-10-12

If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3 xf(x2)dx.

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-10-13Added 95 answers

03xf(x2)dx
Substitute x=u and 2xdx=du
=1203f(x2)(2xdx)
Limits of Integration will change from 03 to 02{(3)2}=09
=1209f(u)du
Remember that abf(u)du=abf(x)dx
=1209f(x)dx=4
=12×4=2
Result: 03xf(x2)dx=2

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