Determine the integrand f(x) if F(x) = x^2+cosx+1

neela | Student

F(x) = x^2+cosx+1.

To find the integrand f(x).

Since the integrand is f(x),

F(x) = integral f(x) dx

Threfore Integral f(x) = F(x),

Integral f(x) dx = x^2+cosx+1.

Differentiating both sides, we get:

f(x) = d/dx {x^2+cosx+1}

f(x) = d/dx (x^2) + d/dx(cosx) +d/dx (1)

f(x) = 2x -sinx +0 , as d/dx(x^n) = nx^(n-1) , d/dx(cosx) = -sinx.

f(x) = 2x-sinx.

giorgiana1976 | Student

The integrand is the result of differentiation of F(x).

Int f(x) dx = F(x)

or

F'(x) = f(x)

Since the integral of f(x) is x^2+cosx+1, then you have to differentiate the result to determine the expression of f(x).

So, we'll calculate the first derivative of the expression resulted after we've integrated f(x).

We'll note the result as F(x) = x^2+cosx+1

F'(x) = (x^2+cosx+1)'

F'(x) = (x^2)' + (cosx)' + (1)'

F'(x) = 2x - sinx + 0

F'(x) = 2 x - sin x

But F'(x) = f(x)

So, f(x) = 2 x - sin x

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