dx secx+C = tan x -1 +C Show that xx -1 sec x+C= -tan -1+C ifx< - 1. First consider the case where x>1. Find a trigonometric substitution for x. Choose the correct answer below. O A. x sec 0 B. x sin e C. x-tan 0 Using the substitution from the previous step, find dx. Substitute forx and dx in the integral. dx = (1) Rewrite the expression in the radical from the previous step using a trigonometric identity, and then simplify the entire integrand. Note that becausex>1, the angle 0 is in the first quadrant. de (Simplify your answer.) Integrate the result from the previous step. dx +C The original indefinite integral is in terms of x, so the final answer must be also in terms of x. Use the trigonometric substitution chosen for this problem to express 0 in terms of x. dx + C -1 Use the answer from the previous step and the reference triangle to the right to find an expression for the integral solution in terms of inverse tangent. V- dx +C Now consider the case where x< -1. Note that in this case, 8 must be restricted to the second quadrant. Using the same procedure as before, find a trigonometric substitution for x, find dx, and make the substitution into the integral. dx = (2) -1 Rewrite the expression in the radical from the previous step using a trigonometric identity, and then simplify the entire integrand. Note that becausex< -1. the angle e is in the second quadrant, and tan e = - tan e de (Simplify your answer.) Integrate the result from the previous step. + C 2/17/2021, 20:
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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