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Staffy
 3 years ago
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)
Staffy
 3 years ago
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)

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RadEn
 3 years ago
Best ResponseYou've already chosen the best response.31) hint : sin^2 x = (1cos2x)/2

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.32) divide 2 case for : Area1 = int (sinx) dx [0,pi] area2 = int(sinx)dx [pi,2pi] the total area is .........

Staffy
 3 years ago
Best ResponseYou've already chosen the best response.0Why is it negative sinx?

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

Staffy
 3 years ago
Best ResponseYou've already chosen the best response.0That makes sense, thanks

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.3let's look this graph dw:1355024687100:dw

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.04) \[\begin{align*} \int\limits_{0}^\pi\sin(mx)\sin(nx)\text dx &=\frac12\int\limits_{0}^\pi\cos((mn)x)\cos((m+n)x)\text dx\\ \\ &=\frac12\left(\frac{\sin((mn)x)}{mn}\frac{\sin((m+n)x)}{m+n}\Big_0^\pi\right)\\ &=\dots\\ &=\dots\\ \\ \end{align*}\]
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