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

2 Answers | Add Yours

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question