Question

Suppose gg is a continuous real-valued function such that 3x5+96=∫g(t)dt3x5+96=∫g(t)dt ( the limit of the integeral from cc to xx ) for each x∈Rx∈R . Where cc is a constant. What is the value of cc ?​

Answer 1

Given:

g is a continuous real-valued function such that 3x^5+96=∫g(t) dt for each  x∈ R and c is a constant.

To Find:

What is the value of c ?​

Solution:

Since, it is given that-

$3x^5+96=\int {g(t)} \, dt$                  .......(1)

Also, we know that , general formula of integration for any function f(x) is

$\int{f(x)} \, dx = g(x) +c$

therefore, $g(x)+c=\int {f(x)} \, dx$ .......(2)

On comparing equation with general formula of integration, we get

$c=96$.

Hence, value of c is 96.