ক্ষেত্রফল নির্ণয়

Letf(x)=sin1(sinx)+cos1(cosx),g(x)=mxandh(x)=xLetf(x)={ sin }^{ -1 }(sin\quad x)+{ cos }^{ -1 }(\quad cos\quad x),\quad g(x)=mx\quad and\quad h(x)=x\quad are three functions. Now g(x) is divided area between f(x),x=π\pi and y=0 into two equal parts.

The area bounded by the curve y=f(x), x=π\pi and y=0 is:

হানি নাটস

Given,

f(x)=sin1sinx+cos1cosx=x+x=2xf(x)=\sin^{-1}\sin x+\cos^{-1}\cos x=x+x=2x

x=πx=\pi

y=0y=0

The above 3 forms a right angled triagle, with center as one vertex.

Area=12 π2πArea=\dfrac{1}{2} \ \pi * 2\pi

=π2sq.units=\pi ^2sq.units

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