Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)f ''(x) = 12x + sin xf(x) =
Question
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)f ''(x) = 12x + sin xf(x) =
Solution
To find the function f(x), we need to integrate f ''(x) twice.
Given f ''(x) = 12x + sin x,
First, we find the first antiderivative f '(x) by integrating f ''(x):
∫f ''(x) dx = ∫(12x + sin x) dx = 6x^2 - cos x + C,
where C is the constant of integration.
Next, we find the second antiderivative f(x) by integrating f '(x):
∫f '(x) dx = ∫(6x^2 - cos x + C) dx = 2x^3 + sin x + Cx + D,
where D is the constant of the second antiderivative.
So, the function f(x) = 2x^3 + sin x + Cx + D.
Similar Questions
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)f(x) = 6x5 − 7x4 − 9x2F(x) =
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)f(x) = 7x + 4 cos xF(x) =
We now must find the antiderivative of f '(x). Even though C is unspecified, the anti-derivative of C will be Cx. Also, a second constant of integration, which we'll call D is required. Thus, we have that the antiderivative of f '(x) = 92x2 − cos x + C is
If f(4) = 11, f ' is continuous, and 6f '(x) dx4 = 18, what is the value of f(6)?f(6) =
Q 60. Find dy/dx, given y = (2tanx * sin2x) / (sec'x - 1) ? Ops: A. •-8cosxsinx B. 0-8cos-x C. © -4cosxsinx D. 0-8cos2x.sin2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.