Evaluate intergral 10xe exponent 10x dx​

for this type of question, integral by parts should be used . This involves using the formula for intregation by parts:

intudv=uv-intvdu.  

lets first break apart the x and e10x into two parts - "u" and "v"

where u = x.

however, we need to find the value of v. in order to do this, we can integrate dv/dx in order to get to v.  

the value of dv/dx is : e10x

u = x             dv/dx = e10x

as seen in the formula, you need to have a value for u, dv, v and du.  

therefore in order to get du you must differentiate u:

u = x    

du/dx = 1

du = 1dx = dx

du = dx

in order to get v you need to integrate dv/dx:

\displaystyle \inte10x dx = 1/10 x10x

now that we have both parts, we can put this back into the formula.  

intudv=uv-intvdu.  

\displaystyle \intxe10x = x * 1/10e10x  - \displaystyle \int1/10e10x dx

Step-by-step explanation:

((10x-1)e^(10x))/10 + C

Step-by-step explanation:

10 integral (xe^(10x)) dx

Integrate by parts f=x f'=1 / g'=e^(10x) g= (e^(10x))/10

(xe^(10x)/10) - integral (e^(10x)/10) dx

Solving integral (e^(10x)/10) dx :

1/100 integral (e^u) du

= e^u/1000 = e^(10x)/100

(xe^(10x)/10)-(e^(10x)/100)

10 integral (xe^(10x)) dx

= xe^(10x)- (e^(10x))/10

= xe^10x - (e^(10x))/10 + C

= ((10x-1)e^(10x))/10 + C

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)