Question

how to evaluate the integral

Answer 1

\[\int\limits_{3}^{4} (4x-7)^{3}\] = \[\int\limits_{a}^{b} f(u) du\]

Answer 2

i need to find a, b, f(u) and evaluate the original integral.

Answer 3

did you try u = 4x - 7 ?

Answer 4

oh ok i got it, a=5, b=9. What would be f(u)? I put u^3 but its wrong.

Answer 5

u = 4x -7
differentiate both sides, what do u get?

Answer 6

du = 4

Answer 7

do you mean du = 4dx??

or du/dx = 4

Answer 8

from that isolate dx

Answer 9

du=4dx
dx=du/4

Answer 10

yes,
if you plug that in your new integral,
you'll get
\(\int_5^9 u^3 \dfrac{du}{4}\)

effectively making f(u) as u^3/4

Answer 11

ah ok, got it. thank you.

Answer 12

welcome ^_^