Problems
In Problems 114, find an antiderivative of the given function.
Evaluate the definite integrals in Problems 1822.
In Problems 2327 an object moves along the yaxis. Given the velocity v, find how far the object moves between the given times t_{0} and t_{1}.

25 
v = 3, f_{0} = 2, t_{1} = 6 
26 
v = 3r^{2}, f_{0} = 1, t_{1} = 3 
27 
v = 10r^{2}, f_{0} = 1, t_{1} = 100 
In Problems 2832, find the area of the region under the curve y = /(x) from a to b.
28 
y = 4 x^{2}, 
a = 2, 
b = 2 
29 

a = 2, 
b = 2 
30 
y = 9x  x^{2}, 
a = 0, 
b = 3 
31 
y = √v  x, 
a = 0, 
b = 1 
32 
y = 3x^{1 3}, 
a = 1, 
b = 8 
33 
If F'(t) = t  1 for all t and F(0) = 2, find F(2). 
34 
If F'(x) = 1  x^{2} for all x and F(3) = 5, find F( 1). 
35 
Suppose F(x) and G(x) have continuous derivatives and F'(x) + G'(x) = 0 for all x. Prove that F(x) + G(x) is constant. 
36 
Suppose F(x) and G(x) have continuous derivatives such that F'(x) < G'(x) for all x. Prove that F(b)  F(a) ≤ G(b)  G(a)
where a < b. 
37 
Prove that a function F(x) has a constant derivative if and only if F(x) is linear, i.e., of the form F(x) = ax + b. 
38 
Prove that a function F(x) has a constant second derivative if and only if F(x) has the form F(x) = ax^{2}+ bx + c. 
39 
Suppose that F"(x) = G"(x) for all x. Prove that F(x) and G(x) differ by a linear function, that is, G(x) = F(x) + ax + b for some real numbers fl and b. 
