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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 ladder 5 meter long rest against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.25 m/s how fast is the top of the ladder slidding down the wall when the bottom of the ladder is 3 cm from the wall?
Define a function that gives the horizontal distance of the tire valve to the right of the tire's vertical diameter ...
If R = 3 m, to what depth must the tank be filled so that it holds 30 m3? Use three iterations of the false-position method to determine your answer. Determine the approximate relative error after each iteration
The function f is graphed below on the interval [0,10].Give the number of valuesc between 0 and 10 which satisfy the conclusion of the mean value theorem for f.
Important information about Probability : Random Selection, A man has been guessing colors of cards drawn from a standard deck of cards. During the first 50 draws he kept track of the number of cards of each color
In a study of milk production in sheep (for use in making cheese), a researcher measured the three-month milk yield for each of 11 ewes. The yields (liters) were as follows.
P-E-M-D-A-S are mnenomic devices for what? What do the underlines in P-E-M-D-A-S REMIND US TO DO? why is it important to be able to remove parentheses?
Multiply and combine like terms - Factor the trinomial and Solve the equation by factoring
Find the equation of the tangent line in slope intercept form of the curve given by: Sand is being poured on a conical pile at the rate of 12 cubic feet per minute, the height of the pile being three times its diameter throughout. At what rate is t..
George has decided that a distribution of data is cubic, that is it has the general form of a function "f(x)=x^3" if the point on the curve that should be at (0,0) is found at (-3,7) and the point.
A 104 inch long piece of wire is cut into two pieces, and two squares are formed. The sum of the areas of the two squares is 388 square inches. If the sides of the squares have integer lengths, what are the lengths of the sides of each square?
Problem 1: The mean of the Standard Normal Distribution is. Problem 2: In a Normal distribution, percent of the data falls below the mean.
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