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(a) Verify that the function defined by $f(x)=\frac{4 e^{4} x^{2} e^{-2 x}}{e^{4}-13}$ over the interval[0,2] is a $p d f$ Find $(b) \operatorname{Pr}(0 \leq x \leq 1),(\text { c) } \operatorname{Pr}(1 \leq x \leq 2) .$ (Note: you do not need to integrate to solve (c).)

(b) 0.424367(c) 0.575633

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 9

Two Integration Techniques

Integrals

Missouri State University

Campbell University

Harvey Mudd College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Let $f(x)=x .$ Find an int…

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01:10

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to tackle this exercise, you're going to need a lot of paper. First off to satisfy these two conditions, we need to have a smaller than zero and B, it's bigger than zero. So we have be the A absolute value after bags equals be today. Um, I was a value x GX. Nothing Cools is gonna start writing a lot of work that I've been working on thinking about this problem. So this is one conclusion will have to look at later. Now we need to do somewhere, um, conditions. If b squared minus a squared is greater than zero. Because we have an absolute values and we have two cases that can happen. Get so when possible. Intervals could be from negatively and discredit to it. B squared minus X squared is bigger than zero. The second case I can happen is that b squared minus a squared. It's bigger than zero. You too, Rachel. The girl Stubble Checking my notes. Lesson zero. Who? The other case we go through the same type of meth again. So then another possible intervals from negative route 2 to 1. So it just depends on each case, so B squared minus six crates less than zero. This is your interval B squared minus a squared is greater than zero. Then you have this interval.

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