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Question

Mathematics Question on applications of integrals

The area bounded by the curves y=y = cos xx and y=y= sin xx between the ordinates x=0x = 0 and x=3π2x = \frac{3\pi}{2} is

A

42+24\sqrt{2}+2

B

4214\sqrt{2}-1

C

42+14\sqrt{2}+1

D

4224\sqrt{2}-2

Answer

4224\sqrt{2}-2

Explanation

Solution

0π4(cosxsinx)dx+π45π4(sinxcosx)dx+5π43π4(cosxsinx)=422\int\limits^{\frac{\pi}{4}}_{0}\left(cos \,x - sin\,x\right)dx +\int\limits^{\frac{5\pi }{4}}_{\frac{\pi}{4}} \left(sin \,x - cos\,x\right)dx +\int\limits^{\frac{3\pi }{4}}_{\frac{5\pi }{4}}\left(cos \,x - sin\,x\right) =4\sqrt{2}-2