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Given $f(x)=\frac{3}{32}\left(4-x^{2}\right)$ over the interval $[-2,2] .$ (a) Show that $f$ is a $p d f$ and determine (b) $\operatorname{Pr}(1 \leq x \leq 2),(\text { c) } \operatorname{Pr}(-1 \leq x \leq 0), \text { (d) } \operatorname{Pr}(|x| \leq 1),$(e) $\operatorname{Pr}(x \leq 1),$ (f) $\operatorname{Pr}(x \geq 0).$

(b) $5 / 32$(c) $11 / 32$(d) $11 / 16$(e) $27 / 32$ (f) $^{1 / 2}$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

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University of Michigan - Ann Arbor

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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.

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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.

01:28

If $f(x)=\left\{\begin{arr…

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If $f^{\prime}(x) \leq 2$ …

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in this video we have a piece of ice, different function F X and they are supposed to find fr zero If our one if I have to nip off three to find a pop zero we look at the input which is zero on If we want to know, zero satisfies in which of these two conditions zero is between minus one and two. So we used these peace to find f off Siddle Be replace x by zero. So we have for syriza going to minus four. Hani's between minus one and two So for finding if one again used this piece and we replace X by one. So we have a one is a gradual minus True, The input true satisfies this condition because in this condition, X can be called to so to find if off to be used This case and we have a physical zero three satisfies this condition because X can be called to three in discussion. Therefore, to find if after baby used this piece on, we replace X by tree so yourself very misty quarter plenty fight. Hope you enjoyed watching this video and thanks for watching

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