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Derivatives IntegralsRelatedRates

VolumesIntegration

ByParts

Take the derivative

of arctan(x/2)

What is 2/(x2+4)?

Take the derivative of 2x

What is 2xln(2)?

Take the derivative of f(g(h(2x3)))

What is f ‘ (g(h(2x3)))*g ‘ (h(2x3))*h ‘ (2x3)*6x2?

If g(x) is the inverse of f(x)

and f(x)=1/(x-1) find g ‘ (2).

What is -1/4?

Take the derivative of arcsin(cos(3x2)).

What is -6xsin(3x2)/√(1-(cos(3x2))2)?

Find the integral of

5x dx.

What is 5x /ln(5) + C?

Find the integral of csc(2x)dx.

What is -1/2ln lcsc(2x)+cot(2x)l + C?

Find the integral of tan(x)dx

What is –ln lcos(x)l + C?

Find the integral of Cos(√t)/(√t)dt.

What is 2sin(√t) + C?

Find the integral of 1/(√1-x2)dx

What is arcsin(x) + C?

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35km/hr

and ship B is sailing north at 25km/hr. How

fast is the distance between the ships

changing at 4 p.m.?

What is 21.4km/hr?

Two cars start moving from the same point. One travels

south at 60mph and the other west at 25mph. At what rate is the distance

between the cars increasing two hours later?

What is 65mph?

At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/hr and ship B is sailing north at 25km/hr. How fast is

the distance between the ships changing at 4p.m.

What is55.4

km/hr?

A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides

away from the wall at a speed of 2ft/sec, how fast is the angle between the top of

the ladder and the wall changing when the angle is

∏/4 radians?

What is√2/5

A water tank has the shape of an inverted circular cone with base radius of 2m and height 4m. If water is being pumped into the tank at a

rate of 2m3/min, find the rate at which the water level is

rising when the water is 3m deep.

What is8/9∏

Find the volume of the resulting solid Y=X2;

X=Y2; about the x-axis.

What is 3∏/10?

Find the volume of the resulting solid Y=X2; X=1; y=0; about the

x-axis.

What is ∏/5?

Find the volume of the enclosed area when revolved about the

line y=1. Y=X; Y=√X

What is ∏/6?

Find the Volume of the rotated solid. Y=X; Y=√X; about X=2

What is 8∏/15?

Find the Volume using shells. Y=sin(x); Y=0; X=2∏; X=3∏; about

the y-axis.

What is ∏/10?

∫x*cos(5x)dx.

What is 1/2x2lnlxl – 1/4x2 + C?

∫arctan(4t)dt

What is t*arctan(4t) – 1/8lnl1+16t2l + C?

∫t3etdt

What is t3et – 3t2et + 6tet – 6et + C?

∫(x*5x)dx

What is 5/ln(5) – 4/(ln(5))2

+ C?

∫(p5*ln(p)) dp

What is 1/6p6

*ln(p) – 1/36*p6 + C?