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greenbadger413Lv1

6 Oct 2020

Evaluate the indefinite integral with constant using -substitution. Then, graph the function and the antiderivative over the indicated interval. If possible, estimate the value of that would need to be added to the antiderivative to make it equal to the definite integral , with the left endpoint of the given interval.

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David MacatangayLv10

12 Nov 2020

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Show transcribed image text This Question: 1 pt 12 of 44 (0 complete) This Quiz: 44 pts possible Verify Property 2 of the definition of a probability density function over the given interval. ffx) 22x What is Property 2 of the definition of a probability density function? O A. The area under the graph of f over the interval [a,bl is b O B. The area under the graph of f over the interval [a.b] is 1 O C. The area under the graph of f over the interval [a,b is a. Since the given interval. [0.oo), has a right-endpoint of infinity, the area under the graph of fwill be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,ool below t(x) dx= lim | f(x) dx= lim [F(x)]a= lim (F(b)-F(a)) b-o0 f(x) dx = lim | f(x) dx = lim [F(x)]-lim (F(a)-F(b)) b- 00 b--0o f(x) dk- lim x) dx- lim [F(x)m (F(b)-F(a)) b-+00
O D. 00 f(x) dx= lim f(x) dx= lim [F(æ£´= lim (F(a)-F(b)) b--oã Substitute a and b into the left side of the formula from the previous step and express the integral as a limit. area 2edx lim2edx Next, determine F(x). First, find the antiderivative of f. 2(Use C as the artbitrary constant.)
Next, determine F(x). First, find the antiderivative of f. as the anbliay cosat) Let C 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,oo) using the far right side of the formula for the area. area = As b approaches oo, e approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step area+1 Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below A Property 2 o the definition o a probability density unction over the given interval has been ver ed since the expression in the previous step simplifies to o B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value. Â° C. â D Property 2 ofthe definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0 Property 2 o the definition o a probability density unction over the given interval has been ve ned since the expressio n e evious ste si plifies to 1.

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