Prove that if f is integrable on [a, b] and c is an element of [a, b], then changing the value of f at c does not change the fact that f is integrable or the value of its integral on [a, b]

Answer with Step-by-step explanation:

We are given that if f is integrable  on [a,b].

c is an element which lie in the interval [a,b]

We have to prove that when we change the value of f at c then the value of f does not change on interval [a,b].

We know that  limit property of an  integral

....(Equation I)

Using above property of integral then we get

......(Equation II)

Substitute equation I and equation II are equal

Then we get

Therefore, .

Hence, the value of function does not change after changing the value of function at c.

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!