Calculus Please Check my answers
posted by Ke$ha .
Use the graph of f(t) = 2t +2 on the interval [−1, 4] to write the function F(x), where
f(x)= integral from 1 to x f(t) dt
f(x)=x^2+3x
f(x)=x^2+2x12 My Answer
f(x)x^2+2x3
f(x)=x^2+4x8
Find the range of the function f(x)=integral from 0 to x (sqrt 4t^2) dt
(0, 4pi)
(0, 2pi) My Answer
(4,0)
(0,4)

Calculus Please Check my answers 
Steve
?[1,x] 2t+2 dt
= t^2+2t [1,x]
= (x^2+2x)(1^2+2*1)
= x^2+2x3
?[0,x] ?(4t^2) dt
= 1/2 ?(4t^2) + 2 arcsin(t/2) [0,x]
= 1/2 ?(4x^2) + 2arcsin(x/2)  (1/2 ?(40) + 2 arcsin(0))
= 1/2 ?(4x^2) + 2arcsin(x/2)  1
The domain is clearly [2,2]
The range is [?1,?1]
http://www.wolframalpha.com/input/?i=range+1%2F2+%E2%88%9A(4x%5E2)+%2B+2arcsin(x%2F2)++1 
Calculus Please Check my answers 
Ke$ha
Well that was my issue with the second one is I originally got that answer but it isn't an option.
Respond to this Question
Similar Questions

calculus
consider the function f(x)= x^2/4 6 Rn is the Riemann sum where the sample points are chosen to be the righthand endpoints of each subinterval. Calculate Rn for f(x)= x^2/4 6 on the interval [0,4] and write your answer as a function … 
calculus
Help! I have a test tommorow! I don't understand (b), (c), (e), and (g). The answers are listed following the each question. Here's a discription of the graph: There is a graph of a function f consists of a semi circle (3 to 1 faced … 
Calculus
I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
calculus II
I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? 
Please Help! Calculus
We have to find out which of these statements are true. I narrowed it down to 2 answers. a) if f"(0)=0, the the graph of f changes concavity at x=0 b) If the function f is continuous on the interval [a,b] and the integral from a to … 
Calculus
Let f be the function defined for x >or= to 0 with f(0)=5 and f', the first derivative of f, give by f'(x)=e^(x/4)sin(x^2). A) Use the graph of f' to determine whether the graph of f is concave up, concave down, or neither on the … 
Math (Integrals)
The area A between the graph of the function: g(t) = 4  (4/t^2) and the taxis over the interval [1, x] is: A(x) = ∫[1, x] (4  (4/t^2)) dt a) Find the horizontal asymptote of the graph g. I believe the horizontal asymptote of graph … 
Calculus help
Use the graph of f(t) = 2t + 2 on the interval [–1, 4] to write the function F(x), where f of x equals the integral from 1 to x of f of t dt. F(x) = x2 + 3x F(x) = x2 + 2x – 12 F(x) = x2 + 2x – 3 F(x) = x2 + 4x – 8