Emma

A particle moves along the x-axis so that at any time t>0 its velocity is given by v(t)=10-3t^2. If the particle is at position x=8 at t=1, what is the position of the particle at t=3?

how do I find the antiderivative of:

secy(tany-secy)

Not really sure how to type this and it wont let me load a pic but:

h(x)=integral (top being 2 and lower being x^2) sqrt(1+t^4) dt. Find h'(1)

would it be:

a. -sqrt2

b. sqrt2

c. -2sqrt2

d. 2sqrt2

e. 4sqrt2

Use a left sum with 4 rectangles of equal width to estimate the area between the graph of f(x)=2x^2 and the x axis between x=0 and x=8

how do I do this, and what is the answer because im coming up with 3 different ones..

Find the upper and lower sums of y=sqrt 1-x^2 on the interval [0,1] partitioned into five subintervals of equal length. Do not use the summation formulas calculate the area of the rectangles directly.

Use the summation formulas to find the exact area between the graph of f(x)=x^2+4 and the x=axis from x=0 to x=2

Could you show your work so I can understand how to solve this? Thanks!!