integration of 9rrdr/1-rrr

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Q. Solve for

r : 27^{6 - r} = 9^{r - 1}

Q. If

\sqrt[r]{\frac{9^{(r + \frac{1}{4})} \sqrt{3 \times 3^{- r}}}{3 \times \sqrt{3^{- r}}}} = m

, then find the value of

m

Q. Assertion :In any

△ A B C

maximum value of

r_{1} + r_{2} + r_{3} = \frac{9 R}{2}

because Reason: In any

△ A B C

R \geq 2 r

$If D_{r} = ⎛ ⎜ ⎝ \begin{matrix} 2^{r - 1} & 2 . 3^{r - 1} & 4 . 5^{r - 1} α & β & γ 2^{n} - 1 & 3^{n} - 1 & 5^{n} - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣, then the value of \sum_{r = 1}^{n} D_{r} is$

Q. If

D_{r} =

∣ ∣ ∣ ∣ ∣ \begin{matrix} r - 1 & n & 6 {(r - 1)}^{2} & 2 n^{2} & 4 n - 2 {(r - 1)}^{3} & 3 n^{3} & 3 n^{2} - 3 n \end{matrix} ∣ ∣ ∣ ∣ ∣

then

n \sum r = 1 D_{r} =

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integration of 9r*r*dr/1-r*r*r

integration of 9rrdr/1-rrr