Determine whether the statement is true or false, and explain why.
integration by parts should be used to evaluate ∫ln(4x) dx.

True

Step-by-step explanation:

The  problem  ∫ln(4x) dx can be solved with integration by parts.

∫ udvdx  = uv − ∫ vdu dx        equ1

where u=ln4x, dv=1dx

       du/dx  = 1/4x      v=x

subtituting those values into the equ 1,we have

 ∫ln(4x) dx = ln4x *x - ∫x*(1/4x)dx

                  = xln4x - ∫(1/4)dx

                  =xln4x- x/4  +C

honesty mood

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)