The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
![\int _D 7xcosydA =7/2(-cos49+1)](https://tex.z-dn.net/?f=%5Cint%20_D%207xcosydA%20%3D7%2F2%28-cos49%2B1%29)
<h3>What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?</h3>
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.
![\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA](https://tex.z-dn.net/?f=%5Cint%20_D%207xcosydA%5C%5C%5C%5C%5Cint%5E7_0%20%5Cint%5Ex%5E2%20_0%207xcosydA)
Integrating we have
![7/2 \int^7_0 (2xsinx^2)dx](https://tex.z-dn.net/?f=7%2F2%20%5Cint%5E7_0%20%282xsinx%5E2%29dx)
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
![7/2 \int^7_0 (2xsinx^2)dx](https://tex.z-dn.net/?f=7%2F2%20%5Cint%5E7_0%20%282xsinx%5E2%29dx)
![7/2 \int^49_0 sin u dx](https://tex.z-dn.net/?f=7%2F2%20%5Cint%5E49_0%20sin%20u%20dx)
Hence
=7/2(-cos49+1)
In conclusion,
![\int _D 7xcosydA =7/2(-cos49+1)](https://tex.z-dn.net/?f=%5Cint%20_D%207xcosydA%20%3D7%2F2%28-cos49%2B1%29)
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