Derivative of the integral from 2 to x of 5x dx?

Answer 1

the derivative of an integral of a function is the function itself
so the answer is 5x, if it was to say by example 2 to x^2, than you need to use chain law, which would change your answer a bit, (multiplying 2x to the function)

Answer 2

Integral 2 to x [5x dx] = 2.5 x^2 evaluated from 2 to x
= 2.5x^2 - 10
So dy/dx = 5x

Answer 3

the integral of 5xdx


5x^2/2 you want x=2 to x


5x^2/2-5*4/2=
5x^2/2-10

Answer 4

Integrate and get (5x^2)/2

Sub in x and get (5x^2)/2

Sub in 2 and get (5*4)/2 = 10

Final answer is (5x^2)/2 - 10

Hope this helps!

Answer 5

f(x) = int(2 to x){5x dx}
f(x) = F(x) - F(2)

Where F(x) = int{5x dx}
F(x) = 5/2 x^2 + C

f(x) = (5/2 x^2 + C) - (5/2 2^2 + C)
f(x) = 5/2 x^2 + C - 5*2 - C
f(x) = 5/2 x^2 - 10
f(x) = 5((x^2 / 2) - 2)