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The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
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