16. What are the values of C0 and C1 in d(t) = C1 + C0t - 16t2, if d(1) = 4 and v(2) = -65?

A) C0 = -1, C1 = 21
B) C0 = 1, C1 = -21
C) C0 = -1, C1 = 19
D) C0 = 0, C1 = 1

17. What does du equal in ∫2x(x2 + 1)5 dx?

A) 2x
B) 2u du
C) 2x dx
D) 5u4

18. What is needed to fully determine an anti-differentiated function?
A) A lot of luck.
B) A boundary condition.
C) What its value is at (0, 0).
D) Its real world application.

19. What is the concavity of f(x) = 3x2 + ½x-1 + 2 @ (-1, 4½)?
A) 5
B) -5
C) 4½
D) 10½

20. What is the one thing done in anti-differentiation that has no counterpart in differentiation?

A) Adding a constant C.
B) Subtracting a constant C.
C) Dividing the new exponent by a constant C.
D) Nothing, they are equally matched step by step.

21.What is the primary difference between using anti-differentiation when finding a definite versus an indefinite integral?

A) Indefinite integrals don't have defined limits.
B) Definite integrals have defined limits.
C) The constant of integration, C.
D) There is no difference between definite and indefinite integrals.

22. What is the second step of performing anti-differentiation?

A) Divide the coefficient by the old exponential value.
B) Subtract the new exponential value from the coefficient.
C) Multiply the coefficient by the new exponential value.
D) Divide the coefficient by the new exponential value.

23. What is the value of R(-4) if:
, f (-4) = 2, h(-4) = 0, f '(-4) = 6, h'(-4) = 3.
A) 0
B) ½
C) 2
D) This is indeterminate.

24. ; what went wrong?

A) Nothing, integralcalculus allows you to have negative areas.
B) Your math is wrong.
C) The function, 3x2 - 12 is below the x-axis along that interval, so it should have been negated first.
D) You had to differentiate the function first, and then fine the absolute value.

25. Which of the following is the best integration technique to use for ∫2x(x2 + 1)5 dx?

A) The product rule.
B) The chain rule.
C) The power rule.
D) The substitution rule.

1. Find the derivatives for the following functions ("^" means "to the power of", sorry I can't do double exponents on my keyboard) :
a. f(X) = 100e10X
b. f(X) = e(10X-5)
c. f(X) = e^X3
d. f(X) = 2X2e^(1- X2)
e. f(X) = 5Xe(12- 2X)
f. f(X) = 100e^(X3 + X4)
g. f(X) = e^(200X - X2 + X100)
2. Fi

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).
2.) Find the volume of the solid of revolution obtained by rotating the region bounded by y = cos x to the power 2, x=0, x = squa

A) If x, y > 0, then ln x - ln y = ln x
¯¯¯¯
ln y
b) If f'(a) = 0 and f"(a) = 0, then the function f does not have an extreme point at x = a.
c) For every real number x, we have ln(e^x²-¹) = (x - 1)(x + 1)
(e

This solution shows how to solve for various calculus problems, including differentiation of functions using the product rule, the quotient rule, and the chain rule, as well as how to calculate integrals.

A 100 ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building?
keywords: integration, integrates, integrals, integrating, double, triple, multiple

1. Consider approximating integrals of the form
I ( f ) = ∫ √x f(x)dx
in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula
∫ √x f(x)dx ≈ w1 f(x1) ≡ I1( f )
which is exact if f(x) is any linear polynomial.
b. To find a formula

Note: * = infinite
Suppose that the function f:[0,*) -> R is continuous and strictly increasing, and that f:(0,*) -> R is differentiable. Moreover, assume f(0) = 0. Consider the formula:
the integral from 0 to x of f + the integral from 0 to f(x) of f^-1 =xf(x) for all x>= 0.
How can I provide a geometric interpretation

GAUSSIAN NUMERICAL INTEGRATION
1. Consider approximating integrals of the form...
in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula... which is exact if f(x) is any linear polynomial.
b. To find a formula... which is exact for all polynomial of degree ≤ 3, set up a system of four e