Advanced Placement (AP), 04.02.2021 05:40 abdullaketbi71

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Answer from: Quest

Repeat the accusation

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The answer is (d) 7/2======we have $f(x) = \begin{cases} x & \text{ for } x \le 0 \\ x + 1 & \text{ for } x \ \textgreater \ 0 \end{cases}$ we also have an integral $\displaystyle\int_{-2}^1 x\, f(x)\; dx$ notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum: $\displaystyle\int_{-2}^1 x\, f(x)\; dx = \displaystyle\int_{-2}^0 x\, f(x)\; dx + \displaystyle\int_{0}^1 x\, f(x)\; dx$ notice that for the piecewise function f, the function has the equationf(x) = x when x ≤ 0. so for the integral $\int_{-2}^0 x\, f(x)\; dx$ , f(x) = x so it changes into $\begin{aligned} \int_{-2}^0 x\, f(x)\; dx & = \int_{-2}^0 x \cdot x\; dx \\ & = \int_{-2}^0 x^2\; dx \\ & = \left[\frac{x^3}{3}\right]_{-2}^0 & & \text{\footnotesize antidifferentiate} \\ & = 0 - \frac{(-2)^3}{3} \\ & = \frac{8}{3} \end{aligned}$ for the piecewise function f, the function has the equationf(x) = x+1 when x > 0. for the integral $\int_{0}^1 x\, f(x)\; dx$ , we have $\begin{aligned} \int_{0}^1 x\, f(x)\; dx & = \int_{0}^1 x(x+1)\; dx \\ & = \int_{0}^1 (x^2+x)\; dx \\ & = \left[ \frac{x^3}{3} + \frac{x^2}{2}\right]_0^1 \\ & = \frac{1}{3} + \frac{1}{2} - 0 = \frac{5}{6} \end{aligned}$ therefore, back to our splitted integral: $\begin{aligned} \displaystyle\int_{-2}^1 x\, f(x)\; dx & = \displaystyle\int_{-2}^0 x\, f(x)\; dx + \displaystyle\int_{0}^1 x\, f(x)\; dx \\ & = \frac{8}{3} + \frac{5}{6} \\ & = \frac{7}{2} \end{aligned}$
Can anyone me on this ap calc question? ?

Can anyone me on this ap calc question? ?

Answer from: Quest

your name

i heard this riddle before

Answer from: Quest

Black minnaloushe’ was maud’s cat (or iseult gonne’s cat…or lady gregory’s cat…depending on which source you credit); nevertheless the cat in this poem can be seen to represent yeats. it is made obvious in other of yeats’ poems from the time that he is unhappy with the fact that he never took enough action (political? pursuing his love for maud? ) and therefore believed himself somewhat predictable and sedentary
‘the moon’ represents maud; in literature the moon is a traditional symbol/metaphor for women – the waxing and waning of the moon having long been associated with the menstrual cycle. other reasons that yeats may have chosen the moon to act as a metaphor for maud is that she was a traveller and a revolutionary – constancy was not her forte! moonlight can also be seen from everywhere and therefore you cannot get away from it. yeats almost feels tormented by maud, not being able to get her off his mind. yet she facilitates his own importance because her moonlight lights the cat – the implication here is that despite his frustrations with her, maud is behind yeats’ greatness. she is the muse which drives his art – without her, neither he nor his poetry, can exist.

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