integral and functions

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If f(x) and Ï†(x) are continuous function in[0,4] satisfying f(x)=f(4-x),Ï†(x) + Ï†(4-x)=3 and âˆ«⁴₀f(x)dx=2,then the value of âˆ«⁴₀ f(x)Ï†(x)dx is:
NOTE:The upper and lower limits are 4 and 0

#Mathematics #Calculus #Relation & Functions

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Manish Shankar ·2014-07-15 01:05:48

I=\int_{0}^{4}f(x)\varphi (x)dx=\int_{0}^{4}f(4-x)\varphi (4-x)dx =\int_{0}^{4}f(x)(3-\varphi (x))dx =\int_{0}^{4}(3f(x)-f(x)\varphi (x))dx

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Sushovan Halder thanks sir
Upvote·0· Reply ·2014-07-15 05:32:45
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integral and functions

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