Please solve Q7

Please solve Q7 If f and g are continuous functions on [O, al such that f(x) = — x) and g(x) + g(a — x) = 2, then show that The value of eS*Xcos3x dx is The value of f cos5 xdx is equal to (D) none of (D) none of th cosx . In(x+ 1 x2 ) dx is equal to The value of J

Dear student
0πesin2x  cos3x dxConsider , esin2x  cos3x dxPut u=sinx=eu21-u2du=eu2-eu2 u2 du=eu2 du-eu2 u2 duUse the common integral eu2 du=eu2 Fu=eu2 Fu-eu2 u2 du=eu2 Fu-eu2 u u  duApply integration by parts : u=u, v'=eu2 u=eu2 Fu-12eu2 u-12eu2 du =eu2 Fu-12eu2 u-12eu2 Fu =esin2x Fsinx-12esin2x sinx-12esin2x Fsinx =-12esin2x sinx+32esin2x Fsinx+CComputing the boundaries0πesin2x  cos3x dx=-12esin2π sinπ+32esin2π Fsinπ--12esin20 sin0+32esin20 Fsin0=32F0-32F0=0

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