To find the antiderivative of f(x) = cos2(5x) , you should re-write f(x) as A. B
ID: 2841927 • Letter: T
Question
To find the antiderivative of f(x) = cos2(5x) , you should re-write f(x) as
A.
B.
C.
D.
If the substitution u = x^2 - 4 is on the definite integral of f(x) from 0 to 6, the new limits of integration are
A. u = 0 and u = - 4
B. u = - 4 and u = 32
C. u = - 4 and u = 6
D. u = 0 and u = 36
Let R be the region bounded by the graph of f and the x - axis on the interval [a, b]. If f is positive on the interval [a, b], then
A. the net area of R equals the area of R.
B. the net area of R is less than the area of R.
C. the net area of R is greater than the area of R.
Let R be the region bounded by the graph of f and the x - axis on the interval [a, b]. Then the net area of Requals the area of R.
True
False
When the region bounded by the graph of f(x) = 3 - 2x and the x - axis on the interval [0, 4] is approximated by left Riemann sums, the aproximations
A. underestimate.
B. overestimate
C. equal the actual area of the region.
D. not enough information to determine.
Without integrating, the average value of f(x) = 3x - 2x^3 on the interval [- 10, 10] is
A. 1
B. 0
C. 3
D. 2
If the substitution u = tan(x) is made, then
dx = sec^2(du)
du = sec^2(x)
du = sec^2(x) dx
du = sec(x) dx
Let A be the average value of f(x) = x^2 on [0, 1] and B be the average value of g(x) = x^3 on [0, 1]. Without integrating is
A. A < B
B. A = B
C. A > B
If A is an area function for f and F is any antiderivative of f, then
A. A = F
B. A = F '
C. f ' = A
D. A ' = f
For the function f(x) = x^2 + 1 on the interval [- 4, 4] how many points on [- 4, 4] satisfy the conclusion of the Mean Value Theorem for Integrals?
A. 1
B. 0
C. 2
The substitution rule is found by reversing the
A. Chain Rule
B. Product Rule
C. Quotient Rule
If A is an area function for f and F is any antiderivative of f, then
A. f ' = A
B. f ' = F
C. f = F + C, where C is an arbitrary constant.
D. F = A + C, where C is an arbitrary constant.
Suppose the interval [1, 3] is subdivided into n = 4 subintervals of equal length. The right Riemann sum uses the grid points is
A. {1, 1.5, 2, 2.5, 3}
B. {1, 1.5, 2, 2.5}
C. {1.5, 2, 2.5, 3}
The best substitution to use to find the antiderivative of cos(x)sin^10(x) is
A. u = sin(10x)
B. u = sin10(x)
C. u = sin(x)
D. u = cos(x)
The sum ( 2^2 + 3^2 + 4^2 ) (1) is a
A. left Riemann sum for f(x) = x^2 on [1, 4] with n = 3.
B. right Riemann sum for f(x) = x^2 on [1, 4] with n = 3.
C. midpoint Riemann sun for f(x) = x^2 on [1, 4] with n = 3.
D. none of the above.
Explanation / Answer
1 d
2 B. u = - 4 and u = 32