If - xma-xndx - k then -a0 xna-xmdx - -

The correct option is B k I=∫_0^af^m(a x)^n #160; dx=k I=∫_0^ax^n(a x)^m #160; dx ∫_0^af(x)^dx=∫_0^af(a x)dx I_1=∫_0^ax^n(a x)^m ...

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Byju's Answer

Standard XII

Mathematics

Property 1

If ∫ xma-xn...

Question

If $\int x^{m} (a - x)^{n} d x = k$
then $\int_{0}^{a} x^{n} (a - x)^{m} d x = ?$

k

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Solution

The correct option is B $k$
$I = \int_{0}^{a} f^{m} (a - x)^{n} d x = k$
$I = \int_{0}^{a} x^{n} (a - x)^{m} d x$
$\int_{0}^{a} f (x)^{d x} = \int_{0}^{a} f (a - x) d x$
$I_{1} = \int_{0}^{a} x^{n} (a - x)^{m} d x = \int_{0}^{a} (a - x)^{n} (x)^{m} d x$
$I = k$
$I_{1} = k$
$\int_{0}^{a} x^{n} (a - x)^{m} d x = k$

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If ∫xm(a−x)ndx=k then ∫a0xn(a−x)mdx=?

The correct option is B kI=∫a0fm(a−x)ndx=kI=∫a0xn(a−x)mdx∫a0f(x)dx=∫a0f(a−x)dxI1=∫a0xn(a−x)mdx=∫a0(a−x)n(x)mdxI=kI1=k∫a0xn(a−x)mdx=k

If $\int x^{m} (a - x)^{n} d x = k$
then $\int_{0}^{a} x^{n} (a - x)^{m} d x = ?$