A few Short Calculus Practice Problems- HELP!

Can anyone please show me how to do these? I'm in short calculus (calc without trig).

If $\displaystyle

\int_1^4 f(x)dx = 6

$ , what is the value of the integral $\displaystyle

\int_1^4 f(5-x)dx $?

A. 6 B. -6 C. 3 D. 0

If $\displaystyle y^2 - 2xy=16$ then $\displaystyle \frac{dy}{dx}=$

a. $\displaystyle \frac{x}{y-x}$ b. $\displaystyle \frac{2y}{y-x}$ c. $\displaystyle \frac{y}{x-y}$ d. $\displaystyle \frac{y}{y-x}$

The area enclosed by $\displaystyle x(1-x)$ and the x axis is

a. 1/6 b. 1 c. 5/6 d/ 2/3

A particle travels in a straight line with a constant acceleration of 3 $\displaystyle \frac{m}{s^2}$. if the velocity of the particle is 10 m/s at time 2s, how far does the particle travel during the time interval when its velocity increases from 4 m/s to 10 m/s

a. 20 b. 14 c. 7 d.6

Let $\displaystyle f(x)=ln\sqrt{x^2+1}$ then f'(1)=

a. 1/3 b. 1/2 c. 3/2 d. 2/3

At what value does the function $\displaystyle f(x)= x^3*e^{-x}$ obtain its maximum value?

a. 3 b. 0 c.e d. √3

Compute $\displaystyle \int_1^4 \sqrt{t}ln t dt $

4ln4_____4/3 ln4______16/3*ln4-28/9______22/3*ln4-25/9

If y is defined at $\displaystyle \frac{dy}{dx}+xy=x$ and y(0)=0, then y(1)=

1-e___1-1/√e_____1-√e_______2-1/√e

On which of the following intervals does $\displaystyle x^5*3x^2+pi=0$ have a solution?

[1,2] [0,1] [-1,0] [-2,-1]

Using the definition of the derivative and the fact that $\displaystyle \frac{d}{dx}a^x = a^x*ln a$, what is the value of the limit of (a^h -1)/h as h approaches 0

ln a 1 DNE a^h*ln a

Determine the equation of the tangent line to y=x-lnx at x=e

For the equation $\displaystyle F(v)= Av^2 + \frac{B}{v^2}$ where a and b are constants, the drag is minimized when v=5. Find the ratio of B/A

Solve the following differential equations:

$\displaystyle \frac{dy}{dx}= \frac{1}{x+1}$ where y(0)=1

$\displaystyle \frac{dy}{dt}=y^2*xe^{-x}$

Integral from +inf to 1 of 1/√x dx

Calculate the following integrals:

$\displaystyle \int \frac{ln{x}}{x^{2}}{dx} =

$

$\displaystyle

\int \frac{1}{\sqrt{x}}$ from 1 to +infinity =

[/tex]

Thanks for any help!