Find the area of the region bounded by the curves?

Question

#y=2\sinx#, #y=2\cosx#, #x=0#, and #x=\pi/2#

↳Redirected from "How do I change #int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx# to cylindrical or spherical coordinates?"

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Answer 1 · 2018-06-02T07:46:54

#4-sqrt(2)#

Solving the equation

#2sin(x)=2*cos(x)#
in the given interval
we get

#x=pi/4#
So our area can be calcultated as

#A=2int_0^(pi/4)sin(x)dx+2int_(pi/4)^(pi/2)cos(x)dx#
this gives
#A=4-2sqrt(2)#