If I- -8747-aa -945- -160-sin5x- -946- -160-tan3x- -947- -160-cos -160-xdx- where alpha- beta- gamma- are constants- then the value depends on-1- gamma- a nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -2- alpha- beta- gamma- a nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -3- alpha- beta- a nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -4- beta-

I= #8747; #945; #945; #945; #160;sin5x+ #946; #160;tan3x+ #947; #160;cos #160;xdx= #945; #160; #8747; #945; #945;sin5x #160;dx ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If I= #8747...

Question

If $I = \int_{- a}^{a} (α \sin^{5} x + β \tan^{3} x + γ \cos x) d x$ , where α, β, γ are constants, then the value depends on
(1) γ, a (2) α, β, γ, a (3) α, β, a (4) β

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Solution

$I = \int_{- α}^{α} (α \sin^{5} x + β \tan^{3} x + γ \cos x) d x = α \int_{- α}^{α} \sin^{5} x d x + β \int_{- α}^{α} \tan^{3} x d x + γ \int_{- α}^{α} \cos x d x N o t e : \sin^{5} x a n d t a n^{3} x a r e o d d f u n c t i o n U s e \int_{- a}^{a} f (x) d x = 0 i f f (x) i s a n o d d f u n c t i o n = 0 + 0 + γ \int_{- α}^{α} \cos x d x = γ \int_{- α}^{α} \cos x d x T h e v a l u e d e p e n d s u p o n o n α a n d γ$

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In each of $α$ $β$ and $γ$ $is a positive acute angle such that$
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If I=∫-aaα sin5x+β tan3x+γ cos xdx, where α, β, γ are constants, then the value depends on (1) γ, a (2) α, β, γ, a (3) α, β, a (4) β

I=∫-ααα sin5x+β tan3x+γ cos xdx=α ∫-ααsin5x dx+β ∫-ααtan3x dx+γ ∫-ααcos xdxNote: sin5x and tan3x are odd functionUse ∫-aafxdx=0 if fx is an odd function=0+0+γ ∫-ααcos xdx=γ ∫-ααcos xdxThe value depends upon on α and γ

If $I = \int_{- a}^{a} (α \sin^{5} x + β \tan^{3} x + γ \cos x) d x$ , where α, β, γ are constants, then the value depends on
(1) γ, a (2) α, β, γ, a (3) α, β, a (4) β