Question

Find a function (f) that satisfies the equation ∫_0^x▒〖f(t)dt=2cos x+3x-2〗

Answer 1

Solution

As I correctly understand the formula in the question is $\int_0^xf(t)dt = 2cosx+3x-2$ .

If $F(x) = \int_0^xf(t)dt$ then f(x) = F’(x).

Therefore f(x) = d(2cosx+3x-2)/dx = -2sinx+3.

Let's check

$\int_0^xf(t)dt = \int_0^x(-2sint+3)dt = (2cost+3t)|_0^x = 2cosx+3x-2cos0 = 2cosx+3x-2$

Answer

f(x) = -2sinx+3