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find the area between curves y=cos (πx÷2) and y=1−x² in the interval [−1,1] Hint: if f(x)is even then f(x)=f(−x)

find the area between curves y=cos (πx÷2) and y=1−x² in the interval [−1,1]   Hint: if f(x)is even then f(x)=f(−x)

Grade:11

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago

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since, from curve you can see the both the function are even valued , you can integrate function between 0 to 1 and take the twice the value of integral, To calculate area integrate
1-x^2-cos (px÷2) between 0 to 1 and take twice of this integral , [x-x^3/3-(2/p)*sin(px÷2)], between 0 and 1, it comes = 1-1/3-(2/p)=.03, and twice this is .06.


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