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Integration tips and tricks - Math 1A, section 103
1. Find 0∫1x dx.
2. What is -3∫3√(9 - x2) dx?
3. Sometimes it helps to simplify an expression before you integrate it. Use this principal to evaluate
1∫5(x2 + 5x + 6/x2 + 3x)dx.
4. Look for familiar derivatives in other integral problems:
(a) 1∫2 2/x dx
(b) 1∫2 (3/1+x2) dx
(c) 1∫2cos(sin(x)) · cos(x) dx
5. Let's see if you can do this one without any tips. Evaluate
0∫π/3(sin(θ) + sin(θ) tan(θ)/sec2(θ)) dθ.
6. Rejoice in your newfound power of prophecy! Suppose you throw a ball upward in the air from a starting height of 2 meters and a starting velocity of 3 meters per second. Given that the Earth's gravity causes the ball to have a constant acceleration of -9.8m/s2, how long will it take for the ball to reach the ground?
A breeding group of foxes is introduced into a protected area, and the population growth follows a logistic pattern. After t years the population of foxes is given by N=39.68/(.30+0.88^t)
A car traveling at 42 ft/sec decelerates at a constant 62feet per second squared. How many feet does the car travel before coming to a complete stop?
How large a surface area in units of square feet will one gallon of paint cover if we apply a coat that is .1 millimeter thick?
Calculate the directional derivative of f at the point (3.0) in the direction (2, -3). What is the maximum directional derivative of f and in what direction does this occur?
the speed of a passenger train is 14 mph faster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 210 miles. Find the speed of each train.
When graphing, assume x = 0 represents the year 2006. What is the trend you observe in the gas prices from 2006 to 2009?
Find the steady-state distribution of the number of machines not working. (c) What is the expected number of operators available for copying?
Find the area A of the region if the length of the side parallel to the river bank is one-half the length of an adjacent side.
Discuss product placement as a tactic in marketing. What are the advantages/disadvantages of this type of promotional tool compared to other types of advertising?
Q: Consider the triangle with vertices at (0,0=x1, (2,0)=x2, and (1,1)=x3. Show that u={(2/3),(1/2)} can be written in the form u=a1x1+a2x2+a3x3, where a_i >= 0, i=1,2,3 and a1+a2+a3=1.
Estimate the change in waiting time if the width is increased to 27 ft and R decreases to 0.35. What is the rate of increase in waiting time per 1-ft increase in width when w = 30 and R = 0.32 vehicle per second?
a)Use Laplace transforms to solve the IVP: y'' + 4y = 0, y(0) = 1, y'(0) = -1 b)Find the Laplace of e^(2t)cos(3t).
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