College Calculus: Find the iterated integral: Integral from 0 to 1 and Integral from x to 1 of cosy^2 dy dx
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College Calculus: Find the iterated integral: Integral from 0 to 1 and Integral from x to 1 of cosy^2 dy dx

[From: ] [author: ] [Date: 12-04-17] [Hit: ]
∫∫D cos(y^2) dA,D = {(x,If you draw this region out,D = {(x,= (1/2)sin(1).I hope this helps!......
I am assuming you wish to compute:
∫∫ cos(y^2) dy dx (from y=x to 1) (from x=0 to 1).

Note that ∫ cos(y^2) dy is a non-elementary integral, so we can cannot compute it. To fix this problem, we need to switch the order of integration.

Note that you can write this integral as:
∫∫D cos(y^2) dA,

where:
D = {(x, y) | 0 <= x <= 1, x <= y <= 1}.

If you draw this region out, you can see that an alternative description of this region is:
D = {(x, y) | 0 <= x <= y, 0 <= y <= 1}.

Thus:
∫∫D cos(y^2) dA = ∫∫ cos(y^2) dx dy (from x=0 to y) (from y=0 to 1)
= ∫ y*cos(y^2) dy (from y=0 to 1) (note that this can integral is easily computed)
= (1/2)sin(y^2) (evaluated from y=0 to 1)
= (1/2)sin(1).

I hope this helps!

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Not to sure if this is what you meant but it sounds like the order of integration must be reversed first..
If I have it correct x Drawing a graph of the boundaries and making it x-simple rather than y simple
the limits become 0 Then by putting the integration becomes a simple substitution as it is cos(y^2)y
1
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