Calculus
posted by Robin .
Consider the function
f(x)=(8)/(x^2)−(8)/(x^5)
.
Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(2) equals ?

F = ∫ 8/x^2  8/x^5 dx
= 8/3 x^3  8/6 x^6 + C
Since F(1) = 0,
8/3 x^3  4/3 x^6 + C = 0
C = 4/3  8/3 = 4/3
F(x) = 8/3 x^3  4/3 x^6  4/3
F(2) = 8/3 (8)  4/3 (64) = 64
Respond to this Question
Similar Questions

math
Consider the function f(t)=2sec^2(t)–6t^2 . Let F(t) be the antiderivative of f(t) with F(0)=0 . Then F(5)=? 
Calculus
Consider the function f(x)=x^4 + 8sqrtx Let F(x) be the antiderivative of f(x) with F(1)=4. Then F(x)=_____ 
Calculus I
Consider the function f(x)=((2)/(x^2))((3)/(x^5)). Let F(x) be the antiderivative of f(x) with F(1) = 0. Find F(3). 
Calculus (Antiderivatives)
Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the above 
Calculus
Consider the function f(x)=4(x−3^2/3. For this function there are two important intervals: (−‡,A) and (A,‡) where A is a critical number. Find A 
Calculus
Consider the function f(x)=(7/x^2)(6/x^6). Let F(x) be the antiderivative of f(x) with F(1)=0. Then F(2) equals _____. 
Calculus Help and Check
1)Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln u where appropriate.) f(x) = (1/5)−(3/x) > (x/5)3lnx+C … 
Calculus
Find f(x) if f′(x)=(−3)⋅x+(−1) and f(−4)=−1. I know if you find the antiderivative of f'(x) it is 3x^2/2  x + c but what do I do next to find the function f(x)? 
calculus
7) Consider the function f(x)=(10/x^2)−(2/x^6). Let F(x) be the antiderivative of f(x) with F(1)=0. Then F(x)= ? 
CALCULUS
Consider the function f(x)=9x3−4x5. Let F(x) be the antiderivative of f(x) with F(1)=0. Then F(4) =