If I-aa-sin 5 x-tan 3 x-cos x dx- where - - - are constants- then the value of I depends on

We have, I= ∫_ a^a(αsin ^5 x+βtan ^3 x+γcos x) d x =α∫_ a^asin ^5 x d x+β∫_ a^atan ^3 x d x+γ∫_ a^acos x d x =α× 0+β× 0+γ× 2 ∫_0^acos x d x =2 γ∫_0^acos x ...

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Standard XII

Mathematics

Integral as Antiderivative

If I=∫-aaαsin...

Question

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

γ, a

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α, β, γ, a

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α, β, a

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β

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Solution

The correct option is A $γ, a$
We have,
$I = a \int - a (α {sin}^{5} x + β {tan}^{3} x + γ cos x) d x = α a \int - a {sin}^{5} x d x + β a \int - a {tan}^{3} x d x + γ a \int - a cos x d x = α \times 0 + β \times 0 + γ \times 2 a \int 0 cos x d x = 2 γ a \int 0 cos x d x ∵ {sin}^{5} x and {tan}^{3} x are odd functions$
$∴ I$ depends on $γ, a$

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Similar questions

Q. lf

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 of I depends on

Q. Let

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (x + α) + i sin (x + α) & cos (x + β) + i sin (x + β) & cos (x + γ) + i sin (x + γ) sin (x + α) - i cos (x + α) & sin (x + β) - i cos (x + β) & sin (x + γ) - i cos (x + γ) sin (2 β - 2 γ) & sin (2 γ - 2 α) & sin (2 α - 2 β) \end{matrix} ∣ ∣ ∣ ∣ ∣

.
Then the value of

f (α) + f (β) - 2 f (γ)

Q. If the points

a (c o s α + i s i n α)

b (c o s β + i s i n β)

and

c (c o s γ + i s i n γ)

are collinear then the value of

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( where

z = b c s i n (β - γ) + c a s i n (γ - α) + a b s i n (α - β) + 3 i - 4 k

)

Q. If the points

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Q. The vertices of an acute angled triangle are

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and

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Integral as Antiderivative

Standard XII Mathematics

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If I=a∫−a(αsin5x+βtan3x+γcosx)dx, where α,β,γ are constants, then the value of I depends on

The correct option is A γ,aWe have, I=a∫−a(αsin5x+βtan3x+γcosx)dx=αa∫−asin5xdx+βa∫−atan3xdx+γa∫−acosxdx=α×0+β×0+γ×2a∫0cosxdx=2γa∫0cosxdx∵sin5x and tan3x are odd functions ∴I depends on γ,a

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