The area bounded by the curves y= x and y= x between the ordinates x=0 and x=32 is:

Question

The area bounded by the curves $y=\cos x$ and $y=\sin x$ between the ordinates $x=0$ and $x=\dfrac{3\pi}{2}$ is:

Accepted Answer

$$\therefore$$ Required area

$$ = \left[ {\int\limits_0^{{\pi  \over 4}} {\left( {\cos \,x - \sin x} \right)dx + } } \right.$$

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\int\limits_{{\pi  \over 4}}^{{5\pi  \over 4}} {\left( {\sin x - \cos x} \right)dx + } $$

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\int\limits_{{5\pi  \over 4}}^{{3\pi  \over 2}} {\left( {\cos x - \sin x} \right)dx  } $$

$$ = 4\sqrt 2  - 2$$

Solutions · 1