Question

The area of one arc of y=sinx+cosx is

Answer 1

Hello friend :-) 

according to your question we need to find area of one arc of y => sinx+cosx 

Now follow my steps what i am doing :=) 

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see the figure it is the one arch of y => sinx +cosx 

now we will do integration to calculate area 

in the graph red line is for cos x and blue line is for sinx 

 To find the shaded area we could calculate the area under the graph of y =

sin x for x between 0 and 1 4π, and subtract this from the area under the

graph of y = cos x between the same limits. Alternatively the two processes

can be combined into one and we can write

                              π/4
shaded area => =    ∫      (cos x − sin x)dx
                               0
                                                        π/4
                             =>    {cosx + sinx } 
                                                         0 

                              =>    cosπ/4 +sinπ/4  - cos0 - sin 0 = >   1/√2 + 1/√2  - 1

                                            (2- √2 ) /√2=> => 0.414. 



HOPE THIS HELPS YOU 

@ engineer gopal IIT roorkey btech :=) 

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Answer 2

Answer. (2- √2 ) /√2=> => 0.414.