数学函数题(英文要好)theareaoftheregionenclosedbythegraphofthepolarcurver=1/(sinx+cosx)andthex-andy-axesis?

Question

数学函数题(英文要好)
the area of the region enclosed by the graph of the polar curve r=1/(sinx+cosx) and the x- and y-axes is ?

Answer 1

求极坐标曲线 r=1/(sinx+cosx) 与X轴和Y轴围成的面积是多少Change r=1/(sinx+cosx) into cartesion coordinates form:把r=1/(sinx+cosx) 变换成直角坐标方程 r(sinx+cosx)=1 r*sinx+r*cosx=1 X+Y=1 Y=0,X=1 X+Y=1 与X轴交点为(0,1) X=0,Y=1,与Y轴交点(1,0),围成三角形面积为:A=1*1/2=1/2 the area is 1/2