Mathematics: 1) (23-36-) + (1) + (8426 را 8 W — ut 13 16 f S x sinly) dx du) too HELLP PLEASE

3 (20+30) means times3×20+3×4060+90...

1) (23-36-) + (1) + (8426 را 8 W — ut 13 16 f S - id1233618426813167161135, kaelycaetano66

emacwhaleng

30.01.2022

Compute the integral with respect to x, then with respect to y:

$\displaystyle16\int_0^\pi\int_0^1x^2\sin y\,\mathrm dx\,\mathrm dy=16\int_0^\pi\sin y\frac{x^3}3\bigg|_0^1\,\mathrm dy$

$=\displaystyle\frac{16}3\int_0^\pi\sin y\,\mathrm dy$

$=\displaystyle\frac{16}3(-\cos y)\bigg|_0^\pi=\boxed{\dfrac{32}3}$

Alternatively, in this case you can "factorize" the integral as

$\displaystyle16\left(\int_0^\pi\sin y\,\mathrm dy\right)\left(\int_0^1x^2\,\mathrm dx\right)$

and get the same result.

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