If -01cos x-1-x d x- Kand -6 -36 -cosx-3-6 -3-x d x-m K then the value of m is

∫_6 π 3^6 πcos (x/3 )/6 π +3 x=3 ∫_2 π 1^2 πcos x/6 π +3 3xdx =3 ∫_ 1^0cos(x+2 π)/6 π +3 3 (x+2 π)dx =3 ∫_ 1^0cos x/3 3xdx = 3 ∫_1^0cos x/3+3xdx=∫_0^1cos x ...

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Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

If ∫01cos x/1...

Question

If $\int_{0}^{1} \frac{c o s x}{1 + x} d x = K a n d \int_{6 π - 3}^{6 π} \frac{c o s (\frac{x}{3})}{6 π + 3 - x} d x = m K$ then the value of m is___

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Solution

$\int_{6 π - 3}^{6 π} \frac{c o s (\frac{x}{3})}{6 π + 3 - x} = 3 \int_{2 π - 1}^{2 π} \frac{c o s x}{6 π + 3 - 3 x} d x = 3 \int_{- 1}^{0} \frac{c o s (x + 2 π)}{6 π + 3 - 3 (x + 2 π)} d x = 3 \int_{- 1}^{0} \frac{c o s x}{3 - 3 x} d x = - 3 \int_{1}^{0} \frac{c o s x}{3 + 3 x} d x = \int_{0}^{1} \frac{c o s x}{1 + x} d x = k$

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Similar questions

I = \int_{π / 6}^{π / 3} \frac{1}{1 + \sqrt{(cot x)}} d x

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then, which one of the following is true?

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If ∫10cosx1+xdx=Kand∫6π6π−3cos(x3)6π+3−xdx=mK then the value of m is___

∫6π6π−3cos(x3)6π+3−x=3∫2π2π−1cosx6π+3−3xdx=3∫0−1cos(x+2π)6π+3−3(x+2π)dx=3∫0−1cosx3−3xdx=−3∫01cosx3+3xdx=∫10cosx1+xdx=k

If $\int_{0}^{1} \frac{c o s x}{1 + x} d x = K a n d \int_{6 π - 3}^{6 π} \frac{c o s (\frac{x}{3})}{6 π + 3 - x} d x = m K$ then the value of m is___