If R -5050 -011- x 50100 dx -011- x 50101 dx- then the value of R isA- 5051B- 5052C- 5053D- 5054

The correct option is A 5051Dr=∫_0^1 (1 x^50)^101.1dx Dr=[x(1 x^50)^101 ]_0^1 ∫_0^1 x(101)[1 x^50]^100( 50x^49)dx =(5050)∫_0^1 (1 x^50)^100[x^50 1+1]dx=Nr ( ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

If R =5050 ∫0...

Question

If $R = \frac{5050 \int_{0}^{1} (1 - x^{50})^{100} d x}{\int_{0}^{1} (1 - x^{50})^{101} d x}$ , then the value of R is

5051

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Solution

The correct option is A 5051
$D r = \int_{0}^{1} (1 - x^{50})^{101} .1 d x D r = {[x (1 - x^{50})^{101}]}_{0}^{50} - \int_{0}^{1} x (101) [1 - x^{50}]^{100} (- 50 x^{49}) d x = (5050) \int_{0}^{1} (1 - x^{50})^{100} [x^{50} - 1 + 1] d x = N r - (5050) D^{r} ∴ R = \frac{N r}{D r} = \frac{N r}{N r - (5050) D r} = \frac{1}{1 - (5050) \frac{D r}{N r}} ∴ R = 5050 + 1 = 5051$

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Similar questions

Q. The value of

\frac{5050 \int_{0}^{1} (1 - x^{50})^{100} d x}{\int_{0}^{1} (1 - x^{50})^{101} d x}

Q. If

I_{1} = \int_{0}^{1} (1 - x^{50})^{100} d x

and

I_{2} = \int_{0}^{1} (1 - x^{50})^{101} d x

such that

I_{2} = α I_{1}

then

α

equals to:

Q. The value of

\frac{(5050) \int_{0}^{1} {(1 - x^{50})}^{100} d x}{\int_{0}^{1} {(1 - x^{50})}^{101} d x}

Q. If

I_{1} = \int_{0}^{1} \frac{1}{| x |} d x

and

I_{2} = \int_{0}^{1} \frac{1}{\sqrt{1 + x^{2}}} d x

, then

If $A = [\begin{matrix} α & 0 1 & 1 \end{matrix}]$ and $B = [\begin{matrix} 1 & 0 3 & 1 \end{matrix}],$ Then the value of $α$ for which $A^{2} = B$ is

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If R=5050∫10(1−x50)100dx∫10(1−x50)101dx, then the value of R is

The correct option is A 5051Dr=∫10(1−x50)101.1dxDr=[x(1−x50)101]10−∫10x(101)[1−x50]100(−50x49)dx=(5050)∫10(1−x50)100[x50−1+1]dx=Nr−(5050)Dr∴R=NrDr=NrNr−(5050)Dr=11−(5050)DrNr∴R=5050+1=5051

If $R = \frac{5050 \int_{0}^{1} (1 - x^{50})^{100} d x}{\int_{0}^{1} (1 - x^{50})^{101} d x}$ , then the value of R is