Initial Value
f'(x)=2x/(x2-1)1/2; (1,1)
f(x)=2(x2-1)1/2+1
Find the area between y=x2 and the x-axis from x=2 and x=4 using 2 intervals and left endpoints of the subintervals
13 square units
f'(x)=x; [0,4]
8
Find the average value of f(x)=2x+3 on the interval x=0 to x=2
5
f'(x)=2x+1-2/x; f(1)=5
f(x)=x2+x-2ln|x|+3
Find the area between y=1/x and the x-axis from x=1 and x=5 using 4 intervals and midpoints of the subintervals.
157/100 or 1.57 square units
f'(x)=x1/2-1; [0,9]
9
Find the average value of f(x)=2x2-3 on the interval x=1 to x=3
17/3 or 5.67
f'(x)=4(2x+2)3; (0,1)
f(x)=1/2(2x+2)4-7
Find the area between y=x-2 and the x-axis from x=2 to x=4 using 4 intervals and left endpoints of the subintervals.
3/2 or 1.5 square units
f'(x)=12x3-9x2+2; [1,6]
3250
Find the average value of f(x)=x2+2x-3 on the interval x=-1 to x=2
-1
In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. If the radius r of the circle is increasing at the rate of r'(t)=30/(2t+4)1/2 ft/min t minutes after the rupture occurs, find an expression for the radius at anytime t. How large is the polluted area 16 minutes after the rupture occurred? hint: r(0)=0
120 ft
Find the area between y=2x and the x-axis from x=2 to x=10 using 5 subintervals and right endpoints
544/5 or 108.8 square units
f'(x)=x2+3x-4; [-1,1]
-22/3 or -7.333
Find the average value of f(x)=1/x+1 on the interval x=0 to x=2
1/2ln(3)
After peaking at 328.9 million British pounds (GBP) in 2008 (t=0), CNP fraud in the UK began to decline at the rate of R(t)=92.07/(t+1) million GBP/year in year t through 2012. What was the amount of CNP fraud on UK-issued credit cards in 2012?
477.08 million British pounds
Find the area between y=1/1+x and the x-axis from x=0 to x=1 using 5 subintervals and left endpoints.
3/4 or .75 square units
Find the area of the region under the graph of f(x)=x1/2 on the interval [1,9]
52/3 or 17.333
Find the average value of f(x)=(2x+1)1/2 on the interval x=0 to x=4
13/6 or 2.167