Calculus I Name:
TA/classroom: Student ID:
Quiz 10
Dec. 26, 2007
1. (5 pts) Use Riemann Sums to compute the given definite integral
∫ 1 0
x2dx
2. (5 pts) Use the Fundamental Theorem to compute the given definite integral
∫ 1 0
x2dx
3. (10 pts) Given F (x) = ∫x2 x
√t2+ 1 dt, use the Fundamental Theorem to compute F0(x)
. .
• Theorem 1.1 If n is any positive integer and c is any constant, then
∑n
i=1
c = cn,
∑n
i=1
i = n(n + 1)
2 ,
∑n
i=1
i2 = n(n + 1)(2n + 1) 6
• Fundamental Theorem of Calculus Part I: If f is continuous on [a, b] and F (x) is any antiderivative of f , then∫b
a f (x)dx = F (b)− F (a).
• Fundamental Theorem of Calculus, Part II: If f is continuous on [a, b] and F (x) =∫ x
a
f (t)dt, then F0(x) = f (x), on [a, b].
