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Staffy
Group Title
Evaluate the following integrals:
sin^2(x)dx from 0 to 2π,
sin x dx from 0 to 2π,
(x^n)(e^−x)dx from 0 to ∞
sin(ax)sin(bx)dx from 0 to π
Consider all possible cases (n is a positive integer)
 one year ago
 one year ago
Staffy Group Title
Evaluate the following integrals: sin^2(x)dx from 0 to 2π, sin x dx from 0 to 2π, (x^n)(e^−x)dx from 0 to ∞ sin(ax)sin(bx)dx from 0 to π Consider all possible cases (n is a positive integer)
 one year ago
 one year ago

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RadEn Group TitleBest ResponseYou've already chosen the best response.3
1) hint : sin^2 x = (1cos2x)/2
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.3
2) divide 2 case for : Area1 = int (sinx) dx [0,pi] area2 = int(sinx)dx [pi,2pi] the total area is .........
 one year ago

Staffy Group TitleBest ResponseYou've already chosen the best response.0
Why is it negative sinx?
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.3
because the absolut function must be positive number, so the area of under xaxes should give a () sign too, so that ()() be postive
 one year ago

Staffy Group TitleBest ResponseYou've already chosen the best response.0
That makes sense, thanks
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.3
let's look this graph dw:1355024687100:dw
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
4) \[\begin{align*} \int\limits_{0}^\pi\sin(mx)\sin(nx)\text dx &=\frac12\int\limits_{0}^\pi\cos((mn)x)\cos((m+n)x)\text dx\\ \\ &=\frac12\left(\frac{\sin((mn)x)}{mn}\frac{\sin((m+n)x)}{m+n}\Big_0^\pi\right)\\ &=\dots\\ &=\dots\\ \\ \end{align*}\]
 one year ago
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